Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
553 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 553 conjugacy classes of subgroups — too many to draw. Only its 67 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×#64266 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | C2×C3⋊(#131⋊C3) | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | C2×C3×GU(2,𝔽3) | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #10593222 | C2 | 1 | 4 | yes | maximal, direct product factor |
| 5 | C2×#5405 | — | 3 | 1 | no | maximal |
| 6 | C2×#4823 | — | 3 | 1 | no | maximal |
| 7 | C2×C3×#41⋊C3 | C22 | 1 | 1 | yes | characteristic |
| 8 | #64266 | C4 | 1 | 2 | yes | complemented |
| 9 | #64266 | C22 | 1 | 2 | yes | — |
| 10 | C2×C3⋊GL(2,𝔽3) | C4 | 1 | 1 | yes | characteristic, complemented |
| 11 | C2×C3⋊#226 | C4 | 1 | 1 | yes | characteristic, complemented |
| 12 | C2×#3712 | — | 4 | 1 | no | maximal |
| 13 | C3⋊(#131⋊C3) | C22 | 1 | 2 | yes | complemented |
| 14 | C3×GU(2,𝔽3) | C22 | 1 | 2 | yes | complemented |
| 15 | C2×#985 | — | 3 | 1 | no | — |
| 16 | C2×#985 | — | 6 | 1 | no | — |
| 17 | C2×#950 | — | 3 | 1 | no | — |
| 18 | C2×#948 | D3 | 1 | 1 | yes | characteristic, complemented |
| 19 | C2×#907 | — | 3 | 1 | no | — |
| 20 | C2×#131⋊C3 | — | 3 | 1 | no | — |
| 21 | C2×GU(2,𝔽3) | D3 | 1 | 1 | yes | characteristic, complemented |
| 22 | #5405 | — | 3 | 4 | no | — |
| 23 | C2×C3×#104 | — | 3 | 1 | no | — |
| 24 | C2×#822 | — | 3 | 1 | no | — |
| 25 | C2×#805 | — | 3 | 1 | no | — |
| 26 | C2×#803 | — | 3 | 1 | no | — |
| 27 | #4823 | — | 3 | 4 | no | — |
| 28 | #4823 | — | 3 | 4 | no | — |
| 29 | C2×C4×C3⋊D3 | — | 4 | 1 | no | — |
| 30 | C3×#41⋊C3 | C2×C4 | 1 | 1 | yes | characteristic |
| 31 | C3×#41⋊C3 | C23 | 1 | 1 | yes | characteristic |
| 32 | C2×C3×SL(2,𝔽3) | C2×C4 | 1 | 1 | yes | characteristic |
| 33 | C3⋊GL(2,𝔽3) | C2×C4 | 1 | 2 | yes | complemented |
| 34 | C3⋊#226 | C2×C4 | 1 | 2 | yes | complemented |
| 35 | C2×C3×C3⋊C8 | — | 4 | 1 | no | — |
| 36 | C2×C3×C3⋊C8 | — | 4 | 1 | no | — |
| 37 | #3712 | — | 4 | 4 | no | — |
| 38 | C2×#444 | — | 9 | 1 | no | Sylow |
| 39 | C2×C3×#41 | C2×D3 | 1 | 1 | yes | characteristic |
| 40 | C2×#235 | — | 3 | 1 | no | — |
| 41 | C2×#41⋊C3 | — | 2 | 1 | no | — |
| 42 | C2×#41⋊C3 | C2×D3 | 1 | 1 | yes | characteristic |
| 43 | #985 | — | 3 | 2 | no | — |
| 44 | #985 | — | 3 | 2 | no | — |
| 45 | #985 | — | 6 | 2 | no | — |
| 46 | #985 | — | 6 | 2 | no | — |
| 47 | C2×GL(2,𝔽3) | — | 3 | 1 | no | — |
| 48 | C2×GL(2,𝔽3) | — | 6 | 1 | no | — |
| 49 | C2×#226 | — | 3 | 1 | no | — |
| 50 | C2×#226 | — | 6 | 1 | no | — |
| 51 | C2×C3×M16 | — | 3 | 1 | no | — |
| 52 | C2×C3×C42 | — | 3 | 1 | no | — |
| 53 | #950 | — | 3 | 2 | no | — |
| 54 | #950 | — | 3 | 2 | no | — |
| 55 | #950 | — | 3 | 2 | no | — |
| 56 | #950 | — | 3 | 2 | no | — |
| 57 | #948 | — | 3 | 2 | no | — |
| 58 | #948 | C2×D3 | 1 | 2 | yes | complemented |
| 59 | C2×#216 | — | 3 | 1 | no | — |
| 60 | C2×#215 | — | 3 | 1 | no | — |
| 61 | C2×#214 | — | 3 | 1 | no | — |
| 62 | C2×#213 | — | 3 | 1 | no | — |
| 63 | C2×#208 | — | 3 | 1 | no | — |
| 64 | C22×C3⋊C8 | — | 3 | 1 | no | — |
| 65 | C22×C3⋊C8 | — | 3 | 1 | no | — |
| 66 | #907 | — | 3 | 4 | no | — |
| 67 | #907 | — | 6 | 2 | no | — |
| 68 | C2×ΓL(1,𝔽25) | — | 6 | 1 | no | — |
| 69 | C2×ΓL(1,𝔽25) | — | 12 | 1 | no | — |
| 70 | C2×D3×C8 | — | 6 | 1 | no | — |
| 71 | #131⋊C3 | — | 3 | 2 | no | — |
| 72 | GU(2,𝔽3) | C2×D3 | 1 | 2 | yes | complemented |
| 73 | C3×#104 | — | 3 | 2 | no | — |
| 74 | C3×#104 | — | 3 | 2 | no | — |
| 75 | #822 | — | 3 | 4 | no | — |
| 76 | #805 | — | 3 | 4 | no | — |
| 77 | #803 | — | 3 | 4 | no | — |
| 78 | C22×C3⋊D3 | — | 4 | 1 | no | — |
| 79 | C2×C32×C4 | — | 4 | 1 | no | — |
| 80 | C2×C3⋊Dic3 | — | 4 | 1 | no | — |
| 81 | C4×C3⋊D3 | — | 4 | 2 | no | — |
| 82 | C4×C3⋊D3 | — | 4 | 2 | no | — |
| 83 | C3×SL(2,𝔽3) | C22×C4 | 1 | 1 | yes | characteristic |
| 84 | C3×C3⋊C8 | — | 4 | 2 | no | — |
| 85 | C3×C3⋊C8 | — | 4 | 2 | no | — |
| 86 | C2×#135 | — | 9 | 1 | no | — |
| 87 | C2×#131 | — | 3 | 1 | no | — |
| 88 | C2×#131 | — | 9 | 1 | no | — |
| 89 | #444 | — | 9 | 4 | no | — |
| 90 | #444 | — | 9 | 4 | no | — |
| 91 | C2×#108 | — | 9 | 1 | no | — |
| 92 | C2×#104 | — | 3 | 1 | no | — |
| 93 | C2×#104 | — | 9 | 1 | no | — |
| 94 | C2×#97 | — | 9 | 1 | no | — |
| 95 | C3×#41 | — | 3 | 1 | no | — |
| 96 | C3×#41 | — | 3 | 1 | no | — |
| 97 | C3×#41 | C4×D3 | 1 | 1 | yes | characteristic |
| 98 | C3×#41 | C22×D3 | 1 | 1 | yes | characteristic |
| 99 | C2×C3×Q8 | C4×D3 | 1 | 1 | yes | characteristic |
| 100 | C2×C3×D4 | — | 3 | 1 | no | — |
| 101 | C22×C3×C4 | — | 3 | 1 | no | — |
| 102 | C22×C3×C4 | — | 6 | 1 | no | — |
| 103 | C2×#67 | — | 6 | 1 | no | — |
| 104 | #235 | — | 3 | 2 | no | — |
| 105 | #235 | — | 3 | 2 | no | — |
| 106 | #235 | — | 6 | 1 | no | — |
| 107 | #235 | — | 6 | 1 | no | — |
| 108 | C2×D12 | — | 3 | 1 | no | — |
| 109 | C2×C4×D3 | — | 6 | 1 | no | — |
| 110 | C2×C4×D3 | — | 12 | 1 | no | — |
| 111 | C2×C4×D3 | — | 24 | 1 | no | — |
| 112 | C2×Dic6 | — | 3 | 1 | no | — |
| 113 | #41⋊C3 | — | 2 | 1 | no | — |
| 114 | #41⋊C3 | — | 2 | 1 | no | — |
| 115 | #41⋊C3 | C4×D3 | 1 | 1 | yes | characteristic |
| 116 | #41⋊C3 | C22×D3 | 1 | 1 | yes | characteristic |
| 117 | C2×SL(2,𝔽3) | — | 2 | 1 | no | — |
| 118 | C2×SL(2,𝔽3) | C4×D3 | 1 | 1 | yes | characteristic |
| 119 | GL(2,𝔽3) | — | 3 | 2 | no | — |
| 120 | GL(2,𝔽3) | — | 6 | 2 | no | — |
| 121 | #226 | — | 3 | 2 | no | — |
| 122 | #226 | — | 6 | 2 | no | — |
| 123 | C3×M16 | — | 3 | 2 | no | — |
| 124 | C3×M16 | — | 6 | 1 | no | — |
| 125 | C2×C3×C8 | — | 6 | 1 | no | — |
| 126 | C2×C3×C8 | — | 12 | 1 | no | — |
| 127 | C3×C42 | — | 3 | 2 | no | — |
| 128 | C3×C42 | — | 6 | 1 | no | — |
| 129 | #216 | — | 3 | 2 | no | — |
| 130 | #216 | — | 3 | 2 | no | — |
| 131 | #215 | — | 3 | 2 | no | — |
| 132 | #215 | — | 3 | 2 | no | — |
| 133 | #214 | — | 3 | 2 | no | — |
| 134 | #214 | — | 3 | 2 | no | — |
| 135 | #213 | — | 3 | 2 | no | — |
| 136 | #213 | — | 3 | 2 | no | — |
| 137 | #208 | — | 3 | 2 | no | — |
| 138 | #208 | — | 6 | 1 | no | — |
| 139 | C2×C3⋊C8 | — | 3 | 2 | no | — |
| 140 | C2×C3⋊C8 | — | 3 | 1 | no | — |
| 141 | C2×C3⋊C8 | — | 3 | 1 | no | — |
| 142 | C2×C3⋊C8 | — | 3 | 2 | no | — |
| 143 | C2×C3⋊C8 | — | 3 | 1 | no | — |
| 144 | C2×C3⋊C8 | — | 3 | 2 | no | — |
| 145 | C2×C3⋊C8 | — | 3 | 2 | no | — |
| 146 | C2×C3⋊C8 | — | 4 | 1 | no | — |
| 147 | C2×C3⋊C8 | S4 | 1 | 1 | yes | characteristic |
| 148 | ΓL(1,𝔽25) | — | 6 | 4 | no | — |
| 149 | ΓL(1,𝔽25) | — | 12 | 4 | no | — |
| 150 | D3×C8 | — | 6 | 4 | no | — |
| 151 | C22×C32 | — | 4 | 1 | no | — |
| 152 | C2×C3⋊D3 | — | 4 | 2 | no | — |
| 153 | C2×C3⋊D3 | — | 8 | 2 | no | — |
| 154 | C32×C4 | — | 4 | 1 | no | — |
| 155 | C32×C4 | — | 4 | 1 | no | — |
| 156 | C3⋊Dic3 | — | 4 | 2 | no | — |
| 157 | C2×#41 | — | 9 | 1 | no | — |
| 158 | C2×#41 | D32 | 1 | 1 | yes | characteristic |
| 159 | #135 | — | 9 | 2 | no | — |
| 160 | #135 | — | 9 | 2 | no | — |
| 161 | #135 | — | 9 | 2 | no | — |
| 162 | #135 | — | 9 | 2 | no | — |
| 163 | C2×Q16 | — | 9 | 1 | no | — |
| 164 | C2×SD16 | — | 9 | 1 | no | — |
| 165 | C2×SD16 | — | 9 | 1 | no | — |
| 166 | C2×D8 | — | 9 | 1 | no | — |
| 167 | #131 | — | 3 | 2 | no | — |
| 168 | #131 | — | 9 | 2 | no | — |
| 169 | #131 | — | 9 | 4 | no | — |
| 170 | #131 | — | 18 | 2 | no | — |
| 171 | C2×M16 | — | 3 | 1 | no | — |
| 172 | C2×M16 | — | 9 | 1 | no | — |
| 173 | C2×M16 | — | 18 | 1 | no | — |
| 174 | C22×C8 | — | 9 | 1 | no | — |
| 175 | C22×C8 | — | 9 | 1 | no | — |
| 176 | C22×C8 | — | 18 | 1 | no | — |
| 177 | C2×C42 | — | 3 | 1 | no | — |
| 178 | #108 | — | 9 | 4 | no | — |
| 179 | #104 | — | 3 | 2 | no | — |
| 180 | #104 | — | 3 | 2 | no | — |
| 181 | #104 | — | 9 | 4 | no | — |
| 182 | #97 | — | 9 | 4 | no | — |
| 183 | C23×C3 | — | 3 | 1 | no | — |
| 184 | C22×D3 | — | 6 | 1 | no | — |
| 185 | C22×D3 | — | 12 | 1 | no | — |
| 186 | C22×D3 | — | 24 | 1 | no | — |
| 187 | C3×Q8 | — | 3 | 1 | no | — |
| 188 | C3×Q8 | C2×C4×D3 | 1 | 1 | yes | characteristic |
| 189 | C3×D4 | — | 3 | 1 | no | — |
| 190 | C3×D4 | — | 3 | 1 | no | — |
| 191 | C3×D4 | — | 6 | 1 | no | — |
| 192 | C2×C3×C4 | — | 3 | 1 | no | — |
| 193 | C2×C3×C4 | — | 3 | 1 | no | — |
| 194 | C2×C3×C4 | — | 3 | 1 | no | — |
| 195 | C2×C3×C4 | — | 3 | 1 | no | — |
| 196 | C2×C3×C4 | — | 3 | 1 | no | — |
| 197 | C2×C3×C4 | — | 4 | 1 | no | — |
| 198 | C2×C3×C4 | — | 6 | 2 | no | — |
| 199 | C2×C3×C4 | — | 8 | 1 | no | — |
| 200 | C2×C3×C4 | — | 12 | 2 | no | — |
| 201 | C2×C3×C4 | C2×S4 | 1 | 1 | yes | characteristic |
| 202 | #67 | — | 6 | 2 | no | — |
| 203 | #67 | — | 6 | 2 | no | — |
| 204 | C2×Dic3 | — | 6 | 1 | no | — |
| 205 | C2×Dic3 | — | 12 | 1 | no | — |
| 206 | C2×Dic3 | — | 24 | 1 | no | — |
| 207 | D12 | — | 3 | 2 | no | — |
| 208 | D12 | — | 6 | 1 | no | — |
| 209 | C4×D3 | — | 6 | 2 | no | — |
| 210 | C4×D3 | — | 6 | 2 | no | — |
| 211 | C4×D3 | — | 12 | 2 | no | — |
| 212 | C4×D3 | — | 12 | 2 | no | — |
| 213 | C4×D3 | — | 24 | 2 | no | — |
| 214 | C4×D3 | — | 24 | 2 | no | — |
| 215 | Dic6 | — | 3 | 2 | no | — |
| 216 | Dic6 | — | 6 | 1 | no | — |
| 217 | SL(2,𝔽3) | — | 2 | 1 | no | — |
| 218 | SL(2,𝔽3) | C2×C4×D3 | 1 | 1 | yes | characteristic |
| 219 | C3×C8 | — | 6 | 2 | no | — |
| 220 | C3×C8 | — | 12 | 2 | no | — |
| 221 | C3⋊C8 | — | 3 | 2 | no | — |
| 222 | C3⋊C8 | — | 3 | 2 | no | — |
| 223 | C3⋊C8 | — | 3 | 2 | no | — |
| 224 | C3⋊C8 | — | 4 | 2 | no | — |
| 225 | C3⋊C8 | C2×S4 | 1 | 2 | yes | — |
| 226 | C2×C32 | — | 4 | 1 | no | — |
| 227 | C2×C32 | — | 4 | 2 | no | — |
| 228 | C3⋊D3 | — | 8 | 2 | no | — |
| 229 | #41 | — | 3 | 1 | no | — |
| 230 | #41 | — | 3 | 1 | no | — |
| 231 | #41 | — | 9 | 2 | no | — |
| 232 | #41 | — | 9 | 2 | no | — |
| 233 | #41 | — | 18 | 1 | no | — |
| 234 | #41 | — | 18 | 1 | no | — |
| 235 | #41 | #624 | 1 | 1 | yes | characteristic |
| 236 | #41 | C2×D32 | 1 | 1 | yes | characteristic |
| 237 | C2×Q8 | — | 9 | 1 | no | — |
| 238 | C2×Q8 | #624 | 1 | 1 | yes | characteristic |
| 239 | C2×D4 | — | 3 | 1 | no | — |
| 240 | C2×D4 | — | 9 | 1 | no | — |
| 241 | C2×D4 | — | 18 | 1 | no | — |
| 242 | C22×C4 | — | 3 | 1 | no | — |
| 243 | C22×C4 | — | 6 | 1 | no | — |
| 244 | C22×C4 | — | 18 | 1 | no | — |
| 245 | Q16 | — | 9 | 2 | no | — |
| 246 | Q16 | — | 9 | 2 | no | — |
| 247 | SD16 | — | 9 | 2 | no | — |
| 248 | SD16 | — | 9 | 2 | no | — |
| 249 | SD16 | — | 9 | 2 | no | — |
| 250 | SD16 | — | 9 | 2 | no | — |
| 251 | D8 | — | 9 | 2 | no | — |
| 252 | D8 | — | 9 | 2 | no | — |
| 253 | M16 | — | 3 | 2 | no | — |
| 254 | M16 | — | 6 | 1 | no | — |
| 255 | M16 | — | 9 | 2 | no | — |
| 256 | M16 | — | 18 | 4 | no | — |
| 257 | M16 | — | 18 | 1 | no | — |
| 258 | C2×C8 | — | 3 | 1 | no | — |
| 259 | C2×C8 | — | 6 | 1 | no | — |
| 260 | C2×C8 | — | 9 | 2 | no | — |
| 261 | C2×C8 | — | 9 | 2 | no | — |
| 262 | C2×C8 | — | 9 | 2 | no | — |
| 263 | C2×C8 | — | 9 | 1 | no | — |
| 264 | C2×C8 | — | 9 | 1 | no | — |
| 265 | C2×C8 | — | 9 | 2 | no | — |
| 266 | C2×C8 | — | 9 | 1 | no | — |
| 267 | C2×C8 | — | 18 | 4 | no | — |
| 268 | C42 | — | 3 | 2 | no | — |
| 269 | C42 | — | 6 | 1 | no | — |
| 270 | C22×C3 | — | 3 | 1 | no | — |
| 271 | C22×C3 | — | 3 | 1 | no | — |
| 272 | C22×C3 | — | 4 | 1 | no | — |
| 273 | C22×C3 | — | 6 | 2 | no | — |
| 274 | C22×C3 | — | 8 | 1 | no | — |
| 275 | C22×C3 | C4×S4 | 1 | 1 | yes | characteristic |
| 276 | C2×D3 | — | 6 | 2 | no | — |
| 277 | C2×D3 | — | 12 | 2 | no | — |
| 278 | C2×D3 | — | 12 | 2 | no | — |
| 279 | C2×D3 | — | 24 | 2 | no | — |
| 280 | C2×D3 | — | 24 | 2 | no | — |
| 281 | C2×D3 | — | 24 | 4 | no | — |
| 282 | C3×C4 | — | 3 | 1 | no | — |
| 283 | C3×C4 | — | 3 | 1 | no | — |
| 284 | C3×C4 | — | 4 | 1 | no | — |
| 285 | C3×C4 | — | 4 | 1 | no | — |
| 286 | C3×C4 | — | 8 | 1 | no | — |
| 287 | C3×C4 | — | 8 | 1 | no | — |
| 288 | C3×C4 | — | 12 | 2 | no | — |
| 289 | C3×C4 | C4×S4 | 1 | 1 | yes | characteristic |
| 290 | C3×C4 | C22×S4 | 1 | 1 | yes | characteristic |
| 291 | Dic3 | — | 6 | 2 | no | — |
| 292 | Dic3 | — | 12 | 2 | no | — |
| 293 | Dic3 | — | 24 | 2 | no | — |
| 294 | C32 | — | 4 | 1 | no | Sylow |
| 295 | C23 | — | 3 | 1 | no | — |
| 296 | C23 | — | 18 | 1 | no | — |
| 297 | Q8 | — | 3 | 1 | no | — |
| 298 | Q8 | — | 9 | 2 | no | — |
| 299 | Q8 | — | 18 | 1 | no | — |
| 300 | Q8 | C2×#624 | 1 | 1 | yes | characteristic |
| 301 | D4 | — | 3 | 1 | no | — |
| 302 | D4 | — | 3 | 1 | no | — |
| 303 | D4 | — | 6 | 1 | no | — |
| 304 | D4 | — | 9 | 2 | no | — |
| 305 | D4 | — | 18 | 1 | no | — |
| 306 | D4 | — | 18 | 2 | no | — |
| 307 | D4 | — | 18 | 2 | no | — |
| 308 | C2×C4 | — | 3 | 1 | no | — |
| 309 | C2×C4 | — | 3 | 1 | no | — |
| 310 | C2×C4 | — | 3 | 1 | no | — |
| 311 | C2×C4 | — | 3 | 1 | no | — |
| 312 | C2×C4 | — | 3 | 1 | no | — |
| 313 | C2×C4 | — | 6 | 2 | no | — |
| 314 | C2×C4 | — | 12 | 2 | no | — |
| 315 | C2×C4 | — | 18 | 1 | no | — |
| 316 | C2×C4 | — | 18 | 2 | no | — |
| 317 | C2×C4 | — | 18 | 2 | no | — |
| 318 | C2×C4 | D3×S4 | 1 | 1 | yes | characteristic |
| 319 | C8 | — | 3 | 2 | no | — |
| 320 | C8 | — | 6 | 2 | no | — |
| 321 | C8 | — | 9 | 2 | no | — |
| 322 | C8 | — | 9 | 2 | no | — |
| 323 | C8 | — | 9 | 2 | no | — |
| 324 | C2×C3 | — | 4 | 1 | no | — |
| 325 | C2×C3 | — | 4 | 2 | no | — |
| 326 | C2×C3 | — | 6 | 1 | no | — |
| 327 | C2×C3 | — | 6 | 1 | no | — |
| 328 | C2×C3 | — | 8 | 1 | no | — |
| 329 | C2×C3 | — | 8 | 2 | no | — |
| 330 | C2×C3 | #5405 | 1 | 2 | yes | complemented |
| 331 | C2×C3 | C2×C4×S4 | 1 | 1 | yes | characteristic |
| 332 | D3 | — | 12 | 2 | no | — |
| 333 | D3 | — | 24 | 2 | no | — |
| 334 | D3 | — | 24 | 4 | no | — |
| 335 | C22 | — | 3 | 1 | no | — |
| 336 | C22 | — | 3 | 1 | no | — |
| 337 | C22 | — | 6 | 2 | no | — |
| 338 | C22 | — | 18 | 2 | no | — |
| 339 | C22 | — | 36 | 2 | no | — |
| 340 | C22 | (C3⋊S4)⋊C4 | 1 | 1 | yes | characteristic |
| 341 | C4 | — | 3 | 1 | no | — |
| 342 | C4 | — | 3 | 1 | no | — |
| 343 | C4 | — | 12 | 2 | no | — |
| 344 | C4 | — | 18 | 2 | no | — |
| 345 | C4 | (C3⋊S4)⋊C4 | 1 | 1 | yes | characteristic |
| 346 | C4 | C2×D3×S4 | 1 | 1 | yes | characteristic |
| 347 | C3 | — | 4 | 1 | no | — |
| 348 | C3 | — | 8 | 1 | no | — |
| 349 | C3 | C2×#5405 | 1 | 1 | yes | characteristic, complemented |
| 350 | C2 | — | 6 | 1 | no | — |
| 351 | C2 | — | 6 | 1 | no | — |
| 352 | C2 | — | 36 | 2 | no | — |
| 353 | C2 | #10593222 | 1 | 2 | yes | direct product factor |
| 354 | C2 | C2×(C3⋊S4)⋊C4 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×C3⋊(#131⋊C3) | C2 | semidirect |
| 3. C2×C3×GU(2,𝔽3) | C2 | semidirect |
| 4. #10593222 | C2 | direct (N × H) |
| 8. #64266 | C4 | semidirect |
| 10. C2×C3⋊GL(2,𝔽3) | C4 | semidirect |
| 11. C2×C3⋊#226 | C4 | semidirect |
| 13. C3⋊(#131⋊C3) | C22 | semidirect |
| 14. C3×GU(2,𝔽3) | C22 | semidirect |
| 18. C2×#948 | D3 | semidirect |
| 21. C2×GU(2,𝔽3) | D3 | semidirect |
| 33. C3⋊GL(2,𝔽3) | C2×C4 | semidirect |
| 34. C3⋊#226 | C2×C4 | semidirect |
| 58. #948 | C2×D3 | semidirect |
| 72. GU(2,𝔽3) | C2×D3 | semidirect |
| 330. C2×C3 | #5405 | semidirect |
| 349. C3 | C2×#5405 | semidirect |
| 353. C2 | #10593222 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#64266 | 2 |
| C2×C3⋊(#131⋊C3) | 2 |
| C2×C3×GU(2,𝔽3) | 2 |
| #10593222 | 2 |
| C2×#5405 | 3 |
| C2×#4823 | 3 |
| C2×#3712 | 4 |