Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
453 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 453 conjugacy classes of subgroups — too many to draw. Only its 51 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | C2×D3×#41⋊C3 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | C2×C3⋊GU(2,𝔽3) | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | C2×C3×GU(2,𝔽3) | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #73149 | — | 3 | 1 | no | maximal |
| 5 | #70380 | — | 3 | 1 | no | maximal |
| 6 | C2×C3×#41⋊C3 | C22 | 1 | 1 | yes | characteristic |
| 7 | D3×#41⋊C3 | — | 2 | 1 | no | — |
| 8 | D3×#41⋊C3 | — | 2 | 1 | no | — |
| 9 | C2×D3×SL(2,𝔽3) | C4 | 1 | 1 | yes | characteristic, complemented |
| 10 | C2×C3⋊(#41⋊C3) | C4 | 1 | 1 | yes | characteristic, complemented |
| 11 | C3⋊GU(2,𝔽3) | — | 2 | 1 | no | — |
| 12 | C3×GU(2,𝔽3) | — | 2 | 1 | no | — |
| 13 | (C2×D3)⋊(C3⋊C8) | — | 4 | 1 | no | maximal |
| 14 | C2×D3×#41 | D3 | 1 | 1 | yes | characteristic |
| 15 | C22×#41⋊C3 | — | 3 | 1 | no | — |
| 16 | C2×GU(2,𝔽3) | — | 3 | 1 | no | — |
| 17 | C2×GU(2,𝔽3) | — | 6 | 1 | no | — |
| 18 | C2×GU(2,𝔽3) | D3 | 1 | 1 | yes | characteristic, complemented |
| 19 | C2×C3×#104 | — | 3 | 1 | no | — |
| 20 | C2×#837 | — | 3 | 1 | no | — |
| 21 | C2×#825 | — | 3 | 1 | no | — |
| 22 | #5126 | — | 3 | 1 | no | — |
| 23 | C4×(C2×D3)⋊C4 | — | 3 | 1 | no | — |
| 24 | C2×#805 | — | 3 | 1 | no | — |
| 25 | C2×C3×C4×D3 | — | 4 | 1 | no | — |
| 26 | C3×#41⋊C3 | D4 | 1 | 1 | yes | characteristic |
| 27 | C3×#41⋊C3 | D4 | 1 | 1 | yes | characteristic |
| 28 | C2×C3×SL(2,𝔽3) | C2×C4 | 1 | 1 | yes | characteristic |
| 29 | D3×SL(2,𝔽3) | — | 2 | 1 | no | — |
| 30 | C3⋊(#41⋊C3) | — | 2 | 1 | no | — |
| 31 | C2×C3⋊(C3⋊C8) | — | 4 | 1 | no | — |
| 32 | C2×C3×C3⋊C8 | — | 4 | 1 | no | — |
| 33 | #1789 | — | 9 | 1 | no | Sylow |
| 34 | C2×C3×#41 | C2×D3 | 1 | 1 | yes | characteristic |
| 35 | D3×#41 | — | 2 | 1 | no | — |
| 36 | D3×#41 | — | 2 | 1 | no | — |
| 37 | D3×#41 | — | 6 | 1 | no | — |
| 38 | D3×#41 | — | 6 | 1 | no | — |
| 39 | C2×#239 | Dic3 | 1 | 1 | yes | characteristic |
| 40 | C2×D3×Q8 | Dic3 | 1 | 1 | yes | characteristic |
| 41 | C2×#237 | — | 3 | 1 | no | — |
| 42 | C2×D3×D4 | — | 3 | 1 | no | — |
| 43 | C2×#235 | — | 3 | 1 | no | — |
| 44 | C22×C4×D3 | — | 3 | 1 | no | — |
| 45 | C2×#41⋊C3 | — | 2 | 1 | no | — |
| 46 | C2×#41⋊C3 | — | 3 | 1 | no | — |
| 47 | C2×#41⋊C3 | — | 6 | 1 | no | — |
| 48 | C2×#41⋊C3 | — | 6 | 1 | no | — |
| 49 | C2×#41⋊C3 | C2×D3 | 1 | 1 | yes | characteristic |
| 50 | C22×SL(2,𝔽3) | — | 3 | 1 | no | — |
| 51 | C2×C3×M16 | — | 3 | 1 | no | — |
| 52 | C2×C3×C42 | — | 3 | 1 | no | — |
| 53 | C2×(C2×D3)⋊C4 | — | 6 | 1 | no | — |
| 54 | C2×C4×Dic3 | — | 3 | 1 | no | — |
| 55 | C2×#208 | — | 3 | 1 | no | — |
| 56 | GU(2,𝔽3) | — | 2 | 1 | no | — |
| 57 | GU(2,𝔽3) | — | 6 | 2 | no | — |
| 58 | GU(2,𝔽3) | — | 6 | 1 | no | — |
| 59 | C3×#104 | — | 6 | 1 | no | — |
| 60 | C3×#104 | — | 6 | 1 | no | — |
| 61 | #837 | — | 6 | 1 | no | — |
| 62 | #837 | — | 6 | 1 | no | — |
| 63 | C3⋊#95 | — | 6 | 1 | no | — |
| 64 | #830 | — | 12 | 1 | no | — |
| 65 | #825 | — | 6 | 2 | no | — |
| 66 | (C2×D3)⋊C8 | — | 6 | 1 | no | — |
| 67 | (C2×D3)⋊C8 | — | 6 | 1 | no | — |
| 68 | #805 | — | 6 | 2 | no | — |
| 69 | C22×C3×D3 | — | 4 | 1 | no | — |
| 70 | C2×C32×C4 | — | 4 | 1 | no | — |
| 71 | C2×C3×Dic3 | — | 4 | 1 | no | — |
| 72 | C3×C4×D3 | — | 8 | 1 | no | — |
| 73 | C3×C4×D3 | — | 8 | 1 | no | — |
| 74 | C3×SL(2,𝔽3) | C22⋊C4 | 1 | 1 | yes | characteristic, complemented |
| 75 | C3⋊(C3⋊C8) | — | 8 | 1 | no | — |
| 76 | C3×C3⋊C8 | — | 8 | 1 | no | — |
| 77 | C22×#41 | — | 3 | 1 | no | — |
| 78 | C2×#104 | — | 3 | 1 | no | — |
| 79 | C2×#104 | — | 9 | 1 | no | — |
| 80 | C2×#104 | — | 9 | 1 | no | — |
| 81 | C2×#104 | — | 9 | 1 | no | — |
| 82 | #407 | — | 9 | 1 | no | — |
| 83 | C4×C22⋊C4 | — | 9 | 1 | no | — |
| 84 | C23×D3 | — | 3 | 1 | no | — |
| 85 | C3×#41 | — | 3 | 1 | no | — |
| 86 | C3×#41 | — | 3 | 1 | no | — |
| 87 | C3×#41 | #67 | 1 | 1 | yes | characteristic |
| 88 | C3×#41 | #67 | 1 | 1 | yes | characteristic |
| 89 | C2×C3×Q8 | C2×Dic3 | 1 | 1 | yes | characteristic |
| 90 | C2×C3×D4 | — | 3 | 1 | no | — |
| 91 | C22×C3×C4 | — | 3 | 1 | no | — |
| 92 | C22×C3×C4 | — | 6 | 1 | no | — |
| 93 | C22×C3×C4 | — | 12 | 1 | no | — |
| 94 | C2×#67 | — | 6 | 1 | no | — |
| 95 | C22×Dic3 | — | 3 | 1 | no | — |
| 96 | C22×Dic3 | — | 6 | 1 | no | — |
| 97 | #239 | — | 2 | 1 | no | — |
| 98 | #239 | — | 6 | 1 | no | — |
| 99 | D3×Q8 | — | 2 | 1 | no | — |
| 100 | D3×Q8 | — | 6 | 1 | no | — |
| 101 | #237 | — | 6 | 2 | no | — |
| 102 | #237 | — | 6 | 1 | no | — |
| 103 | #237 | — | 6 | 1 | no | — |
| 104 | D3×D4 | — | 6 | 2 | no | — |
| 105 | D3×D4 | — | 6 | 1 | no | — |
| 106 | D3×D4 | — | 6 | 1 | no | — |
| 107 | #235 | — | 3 | 2 | no | — |
| 108 | #235 | — | 3 | 2 | no | — |
| 109 | #235 | — | 6 | 1 | no | — |
| 110 | #235 | — | 6 | 1 | no | — |
| 111 | C2×D12 | — | 3 | 1 | no | — |
| 112 | C2×C4×D3 | — | 3 | 1 | no | — |
| 113 | C2×C4×D3 | — | 3 | 1 | no | — |
| 114 | C2×C4×D3 | — | 3 | 1 | no | — |
| 115 | C2×C4×D3 | — | 6 | 1 | no | — |
| 116 | C2×C4×D3 | — | 6 | 1 | no | — |
| 117 | C2×C4×D3 | — | 6 | 1 | no | — |
| 118 | C2×C4×D3 | — | 6 | 1 | no | — |
| 119 | C2×C4×D3 | S4 | 1 | 1 | yes | characteristic |
| 120 | C2×Dic6 | — | 3 | 1 | no | — |
| 121 | #41⋊C3 | — | 2 | 1 | no | — |
| 122 | #41⋊C3 | — | 2 | 1 | no | — |
| 123 | #41⋊C3 | — | 6 | 1 | no | — |
| 124 | #41⋊C3 | D12 | 1 | 1 | yes | characteristic |
| 125 | #41⋊C3 | #67 | 1 | 1 | yes | characteristic |
| 126 | C2×SL(2,𝔽3) | — | 2 | 1 | no | — |
| 127 | C2×SL(2,𝔽3) | — | 6 | 1 | no | — |
| 128 | C2×SL(2,𝔽3) | C4×D3 | 1 | 1 | yes | characteristic |
| 129 | C3×M16 | — | 6 | 1 | no | — |
| 130 | C3×M16 | — | 6 | 1 | no | — |
| 131 | C2×C3×C8 | — | 6 | 1 | no | — |
| 132 | C3×C42 | — | 6 | 1 | no | — |
| 133 | C3×C42 | — | 6 | 1 | no | — |
| 134 | (C2×D3)⋊C4 | — | 6 | 4 | no | — |
| 135 | C4×Dic3 | — | 6 | 1 | no | — |
| 136 | C4×Dic3 | — | 6 | 1 | no | — |
| 137 | #208 | — | 6 | 1 | no | — |
| 138 | #208 | — | 6 | 1 | no | — |
| 139 | C2×C3⋊C8 | — | 4 | 1 | no | — |
| 140 | C2×C3⋊C8 | — | 6 | 1 | no | — |
| 141 | C2×C3⋊C8 | — | 12 | 1 | no | — |
| 142 | C2×C3⋊C8 | — | 24 | 1 | no | — |
| 143 | C22×C32 | — | 4 | 1 | no | — |
| 144 | C2×C3×D3 | — | 4 | 2 | no | — |
| 145 | C2×C3×D3 | — | 8 | 1 | no | — |
| 146 | C2×C3×D3 | — | 8 | 1 | no | — |
| 147 | C32×C4 | — | 4 | 1 | no | — |
| 148 | C32×C4 | — | 4 | 1 | no | — |
| 149 | C3×Dic3 | — | 8 | 1 | no | — |
| 150 | C2×#41 | — | 3 | 1 | no | — |
| 151 | C2×#41 | — | 6 | 1 | no | — |
| 152 | C2×#41 | — | 6 | 1 | no | — |
| 153 | C2×#41 | — | 9 | 1 | no | — |
| 154 | C2×#41 | — | 9 | 1 | no | — |
| 155 | C2×#41 | — | 18 | 1 | no | — |
| 156 | C2×#41 | — | 18 | 1 | no | — |
| 157 | C2×#41 | D32 | 1 | 1 | yes | characteristic |
| 158 | C22×Q8 | — | 3 | 1 | no | — |
| 159 | C22×D4 | — | 9 | 1 | no | — |
| 160 | C23×C4 | — | 9 | 1 | no | — |
| 161 | C2×M16 | — | 3 | 1 | no | — |
| 162 | C2×M16 | — | 9 | 1 | no | — |
| 163 | C2×C22⋊C4 | — | 18 | 1 | no | — |
| 164 | C2×C42 | — | 3 | 1 | no | — |
| 165 | C2×C42 | — | 9 | 1 | no | — |
| 166 | #104 | — | 6 | 1 | no | — |
| 167 | #104 | — | 6 | 1 | no | — |
| 168 | #104 | — | 18 | 2 | no | — |
| 169 | #104 | — | 18 | 2 | no | — |
| 170 | #104 | — | 18 | 1 | no | — |
| 171 | #104 | — | 18 | 1 | no | — |
| 172 | C22⋊C8 | — | 18 | 1 | no | — |
| 173 | C22⋊C8 | — | 18 | 1 | no | — |
| 174 | #95 | — | 18 | 1 | no | — |
| 175 | C23×C3 | — | 3 | 1 | no | — |
| 176 | C23×C3 | — | 12 | 1 | no | — |
| 177 | C22×D3 | — | 3 | 1 | no | — |
| 178 | C22×D3 | — | 6 | 1 | no | — |
| 179 | C22×D3 | — | 6 | 1 | no | — |
| 180 | C22×D3 | — | 6 | 2 | no | — |
| 181 | C22×D3 | — | 12 | 1 | no | — |
| 182 | C22×D3 | SL(2,ℤ/4) | 1 | 1 | yes | characteristic |
| 183 | C3×Q8 | — | 3 | 1 | no | — |
| 184 | C3×Q8 | #217 | 1 | 1 | yes | characteristic |
| 185 | C3×D4 | — | 3 | 1 | no | — |
| 186 | C3×D4 | — | 3 | 1 | no | — |
| 187 | C3×D4 | — | 6 | 1 | no | — |
| 188 | C2×C3×C4 | — | 3 | 1 | no | — |
| 189 | C2×C3×C4 | — | 3 | 1 | no | — |
| 190 | C2×C3×C4 | — | 3 | 1 | no | — |
| 191 | C2×C3×C4 | — | 3 | 1 | no | — |
| 192 | C2×C3×C4 | — | 3 | 1 | no | — |
| 193 | C2×C3×C4 | — | 4 | 1 | no | — |
| 194 | C2×C3×C4 | — | 6 | 2 | no | — |
| 195 | C2×C3×C4 | — | 8 | 1 | no | — |
| 196 | C2×C3×C4 | — | 12 | 1 | no | — |
| 197 | C2×C3×C4 | — | 12 | 1 | no | — |
| 198 | C2×C3×C4 | — | 12 | 1 | no | — |
| 199 | C2×C3×C4 | — | 24 | 1 | no | — |
| 200 | C2×C3×C4 | — | 24 | 1 | no | — |
| 201 | C2×C3×C4 | C2×S4 | 1 | 1 | yes | characteristic |
| 202 | #67 | — | 6 | 2 | no | — |
| 203 | #67 | — | 6 | 2 | no | — |
| 204 | C2×Dic3 | — | 3 | 1 | no | — |
| 205 | C2×Dic3 | — | 6 | 1 | no | — |
| 206 | C2×Dic3 | — | 6 | 1 | no | — |
| 207 | C2×Dic3 | — | 6 | 2 | no | — |
| 208 | C2×Dic3 | — | 12 | 1 | no | — |
| 209 | C2×Dic3 | — | 12 | 1 | no | — |
| 210 | C2×Dic3 | SL(2,ℤ/4) | 1 | 1 | yes | characteristic |
| 211 | D12 | — | 3 | 2 | no | — |
| 212 | D12 | — | 6 | 1 | no | — |
| 213 | C4×D3 | — | 2 | 1 | no | — |
| 214 | C4×D3 | — | 2 | 1 | no | — |
| 215 | C4×D3 | — | 6 | 1 | no | — |
| 216 | C4×D3 | — | 6 | 1 | no | — |
| 217 | C4×D3 | — | 6 | 1 | no | — |
| 218 | C4×D3 | — | 6 | 1 | no | — |
| 219 | C4×D3 | — | 6 | 1 | no | — |
| 220 | C4×D3 | — | 6 | 1 | no | — |
| 221 | Dic6 | — | 3 | 2 | no | — |
| 222 | Dic6 | — | 6 | 1 | no | — |
| 223 | SL(2,𝔽3) | — | 2 | 1 | no | — |
| 224 | SL(2,𝔽3) | (C2×D3)⋊C4 | 1 | 1 | yes | characteristic, complemented |
| 225 | C3×C8 | — | 12 | 1 | no | — |
| 226 | C3⋊C8 | — | 8 | 1 | no | — |
| 227 | C3⋊C8 | — | 12 | 1 | no | — |
| 228 | C3⋊C8 | — | 24 | 1 | no | — |
| 229 | C3⋊C8 | — | 24 | 2 | no | — |
| 230 | C2×C32 | — | 4 | 1 | no | — |
| 231 | C2×C32 | — | 4 | 1 | no | — |
| 232 | C2×C32 | — | 4 | 1 | no | — |
| 233 | C3×D3 | — | 8 | 2 | no | — |
| 234 | C24 | — | 9 | 1 | no | — |
| 235 | #41 | — | 3 | 1 | no | — |
| 236 | #41 | — | 3 | 1 | no | — |
| 237 | #41 | — | 6 | 1 | no | — |
| 238 | #41 | — | 9 | 2 | no | — |
| 239 | #41 | — | 9 | 2 | no | — |
| 240 | #41 | — | 18 | 1 | no | — |
| 241 | #41 | — | 18 | 1 | no | — |
| 242 | #41 | — | 18 | 2 | no | — |
| 243 | #41 | — | 18 | 1 | no | — |
| 244 | #41 | — | 18 | 1 | no | — |
| 245 | #41 | — | 18 | 1 | no | — |
| 246 | #41 | #625 | 1 | 1 | yes | characteristic |
| 247 | #41 | #626 | 1 | 1 | yes | characteristic |
| 248 | C2×Q8 | — | 6 | 1 | no | — |
| 249 | C2×Q8 | — | 9 | 1 | no | — |
| 250 | C2×Q8 | — | 18 | 1 | no | — |
| 251 | C2×Q8 | D3×Dic3 | 1 | 1 | yes | characteristic |
| 252 | C2×D4 | — | 3 | 1 | no | — |
| 253 | C2×D4 | — | 9 | 1 | no | — |
| 254 | C2×D4 | — | 18 | 1 | no | — |
| 255 | C2×D4 | — | 18 | 1 | no | — |
| 256 | C2×D4 | — | 18 | 1 | no | — |
| 257 | C2×D4 | — | 18 | 2 | no | — |
| 258 | C22×C4 | — | 3 | 1 | no | — |
| 259 | C22×C4 | — | 3 | 1 | no | — |
| 260 | C22×C4 | — | 6 | 1 | no | — |
| 261 | C22×C4 | — | 9 | 1 | no | — |
| 262 | C22×C4 | — | 9 | 1 | no | — |
| 263 | C22×C4 | — | 9 | 1 | no | — |
| 264 | C22×C4 | — | 9 | 1 | no | — |
| 265 | C22×C4 | — | 18 | 1 | no | — |
| 266 | C22×C4 | — | 18 | 1 | no | — |
| 267 | C22×C4 | — | 18 | 1 | no | — |
| 268 | C22×C4 | — | 18 | 1 | no | — |
| 269 | C22×C4 | — | 18 | 1 | no | — |
| 270 | M16 | — | 6 | 1 | no | — |
| 271 | M16 | — | 6 | 1 | no | — |
| 272 | M16 | — | 18 | 1 | no | — |
| 273 | M16 | — | 18 | 1 | no | — |
| 274 | C2×C8 | — | 6 | 1 | no | — |
| 275 | C2×C8 | — | 18 | 1 | no | — |
| 276 | C22⋊C4 | — | 18 | 4 | no | — |
| 277 | C42 | — | 6 | 1 | no | — |
| 278 | C42 | — | 6 | 1 | no | — |
| 279 | C42 | — | 18 | 1 | no | — |
| 280 | C42 | — | 18 | 1 | no | — |
| 281 | C22×C3 | — | 3 | 1 | no | — |
| 282 | C22×C3 | — | 3 | 1 | no | — |
| 283 | C22×C3 | — | 4 | 1 | no | — |
| 284 | C22×C3 | — | 6 | 1 | no | — |
| 285 | C22×C3 | — | 6 | 1 | no | — |
| 286 | C22×C3 | — | 8 | 1 | no | — |
| 287 | C22×C3 | — | 12 | 2 | no | — |
| 288 | C22×C3 | — | 24 | 1 | no | — |
| 289 | C22×C3 | — | 24 | 1 | no | — |
| 290 | C22×C3 | C2×SL(2,ℤ/4) | 1 | 1 | yes | characteristic |
| 291 | C2×D3 | — | 2 | 1 | no | — |
| 292 | C2×D3 | — | 2 | 1 | no | — |
| 293 | C2×D3 | — | 6 | 1 | no | — |
| 294 | C2×D3 | — | 6 | 1 | no | — |
| 295 | C2×D3 | — | 6 | 1 | no | — |
| 296 | C2×D3 | — | 12 | 2 | no | — |
| 297 | C2×D3 | — | 12 | 2 | no | — |
| 298 | C2×D3 | GU(2,𝔽3) | 1 | 2 | yes | complemented |
| 299 | C3×C4 | — | 3 | 1 | no | — |
| 300 | C3×C4 | — | 3 | 1 | no | — |
| 301 | C3×C4 | — | 4 | 1 | no | — |
| 302 | C3×C4 | — | 4 | 1 | no | — |
| 303 | C3×C4 | — | 8 | 1 | no | — |
| 304 | C3×C4 | — | 8 | 1 | no | — |
| 305 | C3×C4 | — | 12 | 2 | no | — |
| 306 | C3×C4 | — | 24 | 1 | no | — |
| 307 | C3×C4 | GL(2,ℤ/4) | 1 | 1 | yes | characteristic |
| 308 | C3×C4 | GL(2,ℤ/4) | 1 | 1 | yes | characteristic |
| 309 | Dic3 | — | 2 | 1 | no | — |
| 310 | Dic3 | — | 6 | 1 | no | — |
| 311 | Dic3 | — | 12 | 2 | no | — |
| 312 | C32 | — | 4 | 1 | no | Sylow |
| 313 | C23 | — | 3 | 1 | no | — |
| 314 | C23 | — | 3 | 1 | no | — |
| 315 | C23 | — | 9 | 1 | no | — |
| 316 | C23 | — | 18 | 2 | no | — |
| 317 | C23 | — | 18 | 1 | no | — |
| 318 | C23 | — | 18 | 1 | no | — |
| 319 | C23 | — | 36 | 1 | no | — |
| 320 | Q8 | — | 3 | 1 | no | — |
| 321 | Q8 | — | 9 | 2 | no | — |
| 322 | Q8 | — | 18 | 1 | no | — |
| 323 | Q8 | (C2×D3)⋊Dic3 | 1 | 1 | yes | characteristic |
| 324 | D4 | — | 3 | 1 | no | — |
| 325 | D4 | — | 3 | 1 | no | — |
| 326 | D4 | — | 6 | 1 | no | — |
| 327 | D4 | — | 9 | 2 | no | — |
| 328 | D4 | — | 18 | 1 | no | — |
| 329 | D4 | — | 18 | 2 | no | — |
| 330 | D4 | — | 18 | 2 | no | — |
| 331 | C2×C4 | — | 3 | 1 | no | — |
| 332 | C2×C4 | — | 3 | 1 | no | — |
| 333 | C2×C4 | — | 3 | 1 | no | — |
| 334 | C2×C4 | — | 3 | 1 | no | — |
| 335 | C2×C4 | — | 3 | 1 | no | — |
| 336 | C2×C4 | — | 3 | 1 | no | — |
| 337 | C2×C4 | — | 6 | 1 | no | — |
| 338 | C2×C4 | — | 6 | 1 | no | — |
| 339 | C2×C4 | — | 6 | 2 | no | — |
| 340 | C2×C4 | — | 9 | 1 | no | — |
| 341 | C2×C4 | — | 12 | 1 | no | — |
| 342 | C2×C4 | — | 12 | 1 | no | — |
| 343 | C2×C4 | — | 18 | 1 | no | — |
| 344 | C2×C4 | — | 18 | 1 | no | — |
| 345 | C2×C4 | — | 18 | 1 | no | — |
| 346 | C2×C4 | — | 18 | 1 | no | — |
| 347 | C2×C4 | — | 18 | 1 | no | — |
| 348 | C2×C4 | — | 18 | 1 | no | — |
| 349 | C2×C4 | — | 18 | 1 | no | — |
| 350 | C2×C4 | — | 18 | 1 | no | — |
| 351 | C2×C4 | — | 18 | 2 | no | — |
| 352 | C2×C4 | — | 36 | 1 | no | — |
| 353 | C2×C4 | — | 36 | 1 | no | — |
| 354 | C2×C4 | D3×S4 | 1 | 1 | yes | characteristic |
| 355 | C8 | — | 12 | 1 | no | — |
| 356 | C8 | — | 36 | 1 | no | — |
| 357 | C2×C3 | — | 4 | 1 | no | — |
| 358 | C2×C3 | — | 4 | 1 | no | — |
| 359 | C2×C3 | — | 4 | 1 | no | — |
| 360 | C2×C3 | — | 6 | 1 | no | — |
| 361 | C2×C3 | — | 6 | 1 | no | — |
| 362 | C2×C3 | — | 8 | 1 | no | — |
| 363 | C2×C3 | — | 8 | 1 | no | — |
| 364 | C2×C3 | — | 8 | 1 | no | — |
| 365 | C2×C3 | — | 24 | 2 | no | — |
| 366 | C2×C3 | C2×GU(2,𝔽3) | 1 | 1 | yes | characteristic |
| 367 | C2×C3 | #5423 | 1 | 1 | yes | characteristic |
| 368 | C2×C3 | #5432 | 1 | 1 | yes | characteristic |
| 369 | D3 | — | 2 | 2 | no | — |
| 370 | D3 | — | 12 | 1 | no | — |
| 371 | C22 | — | 3 | 2 | no | — |
| 372 | C22 | — | 3 | 1 | no | — |
| 373 | C22 | — | 3 | 1 | no | — |
| 374 | C22 | — | 6 | 1 | no | — |
| 375 | C22 | — | 6 | 1 | no | — |
| 376 | C22 | — | 6 | 1 | no | — |
| 377 | C22 | — | 6 | 1 | no | — |
| 378 | C22 | — | 18 | 1 | no | — |
| 379 | C22 | — | 18 | 1 | no | — |
| 380 | C22 | — | 18 | 1 | no | — |
| 381 | C22 | — | 36 | 2 | no | — |
| 382 | C22 | — | 36 | 2 | no | — |
| 383 | C22 | D3×SL(2,ℤ/4) | 1 | 1 | yes | characteristic |
| 384 | C4 | — | 3 | 1 | no | — |
| 385 | C4 | — | 3 | 1 | no | — |
| 386 | C4 | — | 6 | 1 | no | — |
| 387 | C4 | — | 12 | 2 | no | — |
| 388 | C4 | — | 18 | 1 | no | — |
| 389 | C4 | — | 36 | 2 | no | — |
| 390 | C4 | #64209 | 1 | 1 | yes | characteristic |
| 391 | C4 | #64210 | 1 | 1 | yes | characteristic |
| 392 | C3 | — | 4 | 1 | no | — |
| 393 | C3 | — | 8 | 1 | no | — |
| 394 | C3 | #73149 | 1 | 1 | yes | characteristic, complemented |
| 395 | C2 | — | 6 | 1 | no | — |
| 396 | C2 | — | 6 | 1 | no | — |
| 397 | C2 | — | 6 | 2 | no | — |
| 398 | C2 | — | 36 | 1 | no | — |
| 399 | C2 | D3×GU(2,𝔽3) | 1 | 1 | yes | characteristic |
| 400 | C2 | #10593228 | 1 | 1 | yes | characteristic |
| 401 | C2 | (C2×D3)⋊SL(2,ℤ/4) | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×C3⋊GU(2,𝔽3) | C2 | semidirect |
| 3. C2×C3×GU(2,𝔽3) | C2 | semidirect |
| 9. C2×D3×SL(2,𝔽3) | C4 | semidirect |
| 10. C2×C3⋊(#41⋊C3) | C4 | semidirect |
| 18. C2×GU(2,𝔽3) | D3 | semidirect |
| 74. C3×SL(2,𝔽3) | C22⋊C4 | semidirect |
| 224. SL(2,𝔽3) | (C2×D3)⋊C4 | semidirect |
| 298. C2×D3 | GU(2,𝔽3) | semidirect |
| 394. C3 | #73149 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D3×#41⋊C3 | 2 |
| C2×C3⋊GU(2,𝔽3) | 2 |
| C2×C3×GU(2,𝔽3) | 2 |
| #73149 | 3 |
| #70380 | 3 |
| (C2×D3)⋊(C3⋊C8) | 4 |