Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
509 conjugacy classes of subgroups; only the 64 normal subgroups are shown.
This group has 509 conjugacy classes of subgroups — too many to draw. Only its 64 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 | C3×#5927 | C2 | 1 | 2 | yes | maximal, complemented |
| 2 | C3×#578⋊C3 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | C3×#5430 | C2 | 1 | 2 | yes | maximal, complemented |
| 4 | C3×#5404 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | C3×#5403 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #85475 | C3 | 1 | 1 | yes | maximal, characteristic, direct product factor |
| 7 | C3×#3293 | — | 3 | 1 | no | maximal |
| 8 | C3×2−1+4⋊C3 | C22 | 1 | 2 | yes | — |
| 9 | C3×#985 | C22 | 1 | 1 | yes | characteristic |
| 10 | C3×#984 | C22 | 1 | 2 | yes | — |
| 11 | C3×#983 | — | 2 | 2 | no | — |
| 12 | C2×C3×#226 | — | 2 | 2 | no | — |
| 13 | C3×#912 | — | 4 | 1 | no | maximal |
| 14 | C3×#131⋊C3 | C22 | 1 | 1 | yes | characteristic |
| 15 | C3×GU(2,𝔽3) | C22 | 1 | 1 | yes | characteristic |
| 16 | #5927 | C2×C3 | 1 | 2 | yes | complemented |
| 17 | C3×#578 | — | 3 | 1 | no | — |
| 18 | C3×#578 | — | 3 | 2 | no | — |
| 19 | C3×#578 | D3 | 1 | 1 | yes | characteristic, complemented |
| 20 | #578⋊C3 | — | 2 | 1 | no | — |
| 21 | #578⋊C3 | C2×C3 | 1 | 1 | yes | characteristic, complemented |
| 22 | #5430 | C2×C3 | 1 | 2 | yes | complemented |
| 23 | #5404 | C2×C3 | 1 | 1 | yes | characteristic, complemented |
| 24 | #5403 | C2×C3 | 1 | 1 | yes | characteristic, complemented |
| 25 | C3×#494 | — | 3 | 1 | no | — |
| 26 | C3×#473 | — | 3 | 1 | no | — |
| 27 | C3×#473 | — | 3 | 2 | no | — |
| 28 | C3×#473 | — | 3 | 1 | no | — |
| 29 | C3×#456 | — | 3 | 2 | no | — |
| 30 | C3×#456 | — | 3 | 2 | no | — |
| 31 | C3×#443 | — | 3 | 1 | no | — |
| 32 | C3×#443 | — | 3 | 1 | no | — |
| 33 | C3×#237 | — | 4 | 2 | no | — |
| 34 | C3×#41⋊C3 | C23 | 1 | 1 | yes | characteristic |
| 35 | C2×C3×SL(2,𝔽3) | — | 2 | 2 | no | — |
| 36 | C3×GL(2,𝔽3) | D4 | 1 | 1 | yes | characteristic |
| 37 | C3×#226 | — | 2 | 2 | no | — |
| 38 | C3×#226 | D4 | 1 | 1 | yes | characteristic |
| 39 | C32×D8 | — | 4 | 1 | no | — |
| 40 | C3×#214 | — | 4 | 2 | no | — |
| 41 | C3×Dic12 | — | 4 | 1 | no | — |
| 42 | C3×D3×C8 | — | 4 | 1 | no | — |
| 43 | #3293 | — | 3 | 1 | no | Sylow |
| 44 | C3×2−1+4 | — | 3 | 2 | no | — |
| 45 | C3×2−1+4 | C2×D3 | 1 | 2 | yes | — |
| 46 | 2−1+4⋊C3 | — | 2 | 2 | no | — |
| 47 | 2−1+4⋊C3 | C22×C3 | 1 | 2 | yes | — |
| 48 | #985 | C22×C3 | 1 | 1 | yes | characteristic |
| 49 | #984 | C22×C3 | 1 | 2 | yes | — |
| 50 | #983 | — | 2 | 2 | no | — |
| 51 | C2×#226 | — | 2 | 2 | no | — |
| 52 | C3×#137 | — | 3 | 2 | no | — |
| 53 | C3×#137 | — | 3 | 2 | no | — |
| 54 | C3×#137 | — | 3 | 2 | no | — |
| 55 | C3×#137 | — | 3 | 2 | no | — |
| 56 | C3×#137 | — | 6 | 2 | no | — |
| 57 | C3×#137 | — | 6 | 2 | no | — |
| 58 | C3×#137 | — | 6 | 2 | no | — |
| 59 | C3×#135 | — | 3 | 1 | no | — |
| 60 | C3×#135 | — | 3 | 1 | no | — |
| 61 | C3×#135 | — | 6 | 2 | no | — |
| 62 | C3×#135 | — | 6 | 1 | no | — |
| 63 | C2×C3×Q16 | — | 3 | 1 | no | — |
| 64 | C2×C3×Q16 | — | 3 | 2 | no | — |
| 65 | C2×C3×Q16 | — | 3 | 1 | no | — |
| 66 | C2×C3×Q16 | — | 6 | 2 | no | — |
| 67 | C2×C3×Q16 | — | 6 | 1 | no | — |
| 68 | C3×#131 | — | 3 | 2 | no | — |
| 69 | C3×#131 | — | 3 | 1 | no | — |
| 70 | C3×#131 | C2×D3 | 1 | 1 | yes | characteristic |
| 71 | C3×C4⋊Q8 | — | 3 | 2 | no | — |
| 72 | #912 | — | 4 | 1 | no | — |
| 73 | #131⋊C3 | — | 2 | 1 | no | — |
| 74 | #131⋊C3 | C22×C3 | 1 | 1 | yes | characteristic |
| 75 | GU(2,𝔽3) | C22×C3 | 1 | 1 | yes | characteristic |
| 76 | C3×#108 | — | 3 | 1 | no | — |
| 77 | C3×#108 | — | 3 | 1 | no | — |
| 78 | C3×#104 | — | 3 | 1 | no | — |
| 79 | C3×#104 | — | 3 | 2 | no | — |
| 80 | C3×#104 | — | 3 | 1 | no | — |
| 81 | C3×#101 | — | 3 | 2 | no | — |
| 82 | C3×#101 | — | 3 | 2 | no | — |
| 83 | C3×C4×C8 | — | 3 | 1 | no | — |
| 84 | C32×D4 | — | 4 | 2 | no | — |
| 85 | C3×#67 | — | 8 | 2 | no | — |
| 86 | C2×C3×Dic3 | — | 8 | 2 | no | — |
| 87 | C3×C4×D3 | — | 4 | 1 | no | — |
| 88 | C3×Dic6 | — | 4 | 2 | no | — |
| 89 | C3×SL(2,𝔽3) | C2×D4 | 1 | 1 | yes | characteristic |
| 90 | C32×C8 | — | 4 | 1 | no | — |
| 91 | C3×C3⋊C8 | — | 4 | 1 | no | — |
| 92 | #578 | — | 3 | 1 | no | — |
| 93 | #578 | — | 3 | 2 | no | — |
| 94 | #578 | C3×D3 | 1 | 1 | yes | characteristic, complemented |
| 95 | #494 | — | 3 | 1 | no | — |
| 96 | #473 | — | 3 | 1 | no | — |
| 97 | #473 | — | 3 | 2 | no | — |
| 98 | #473 | — | 3 | 1 | no | — |
| 99 | #456 | — | 3 | 2 | no | — |
| 100 | #456 | — | 3 | 2 | no | — |
| 101 | #443 | — | 3 | 1 | no | — |
| 102 | #443 | — | 3 | 1 | no | — |
| 103 | C3×#41 | — | 3 | 1 | no | — |
| 104 | C3×#41 | — | 3 | 2 | no | — |
| 105 | C3×#41 | — | 6 | 2 | no | — |
| 106 | C3×#41 | — | 6 | 2 | no | — |
| 107 | C3×#41 | — | 6 | 2 | no | — |
| 108 | C3×#41 | — | 12 | 2 | no | — |
| 109 | C3×#41 | C22×D3 | 1 | 1 | yes | characteristic |
| 110 | C2×C3×Q8 | — | 2 | 2 | no | — |
| 111 | C2×C3×Q8 | — | 3 | 2 | no | — |
| 112 | C2×C3×Q8 | — | 3 | 2 | no | — |
| 113 | C2×C3×Q8 | — | 6 | 2 | no | — |
| 114 | C2×C3×Q8 | — | 6 | 2 | no | — |
| 115 | #237 | — | 4 | 2 | no | — |
| 116 | #41⋊C3 | — | 2 | 1 | no | — |
| 117 | #41⋊C3 | C23×C3 | 1 | 1 | yes | characteristic |
| 118 | C2×SL(2,𝔽3) | — | 2 | 2 | no | — |
| 119 | C2×SL(2,𝔽3) | — | 4 | 2 | no | — |
| 120 | GL(2,𝔽3) | C3×D4 | 1 | 1 | yes | characteristic |
| 121 | #226 | — | 2 | 2 | no | — |
| 122 | #226 | C3×D4 | 1 | 1 | yes | characteristic |
| 123 | C3×Q16 | — | 3 | 1 | no | — |
| 124 | C3×Q16 | — | 3 | 1 | no | — |
| 125 | C3×Q16 | — | 6 | 1 | no | — |
| 126 | C3×Q16 | — | 6 | 2 | no | — |
| 127 | C3×Q16 | — | 6 | 2 | no | — |
| 128 | C3×Q16 | — | 6 | 1 | no | — |
| 129 | C3×Q16 | — | 6 | 2 | no | — |
| 130 | C3×Q16 | — | 6 | 2 | no | — |
| 131 | C3×Q16 | — | 6 | 2 | no | — |
| 132 | C3×Q16 | — | 6 | 1 | no | — |
| 133 | C3×SD16 | — | 3 | 1 | no | — |
| 134 | C3×SD16 | — | 3 | 1 | no | — |
| 135 | C3×SD16 | — | 3 | 2 | no | — |
| 136 | C3×SD16 | — | 6 | 2 | no | — |
| 137 | C3×SD16 | — | 6 | 2 | no | — |
| 138 | C3×SD16 | — | 6 | 2 | no | — |
| 139 | C3×D8 | — | 3 | 1 | no | — |
| 140 | C3×D8 | — | 4 | 1 | no | — |
| 141 | C3×D8 | — | 8 | 1 | no | — |
| 142 | C3×D8 | S4 | 1 | 1 | yes | characteristic |
| 143 | C3×M16 | — | 3 | 1 | no | — |
| 144 | C3×M16 | — | 3 | 2 | no | — |
| 145 | C3×M16 | — | 3 | 1 | no | — |
| 146 | C3×M16 | — | 6 | 2 | no | — |
| 147 | C3×M16 | — | 6 | 1 | no | — |
| 148 | C2×C3×C8 | — | 3 | 1 | no | — |
| 149 | C2×C3×C8 | — | 3 | 1 | no | — |
| 150 | C2×C3×C8 | — | 6 | 2 | no | — |
| 151 | C2×C3×C8 | — | 6 | 1 | no | — |
| 152 | C3×C4⋊C4 | — | 12 | 2 | no | — |
| 153 | C3×C42 | — | 3 | 1 | no | — |
| 154 | #214 | — | 4 | 2 | no | — |
| 155 | Dic12 | — | 4 | 1 | no | — |
| 156 | D3×C8 | — | 4 | 1 | no | — |
| 157 | C22×C32 | — | 8 | 2 | no | — |
| 158 | C2×C3×D3 | — | 4 | 1 | no | — |
| 159 | C32×C4 | — | 4 | 1 | no | — |
| 160 | C3×Dic3 | — | 4 | 1 | no | — |
| 161 | C3×Dic3 | — | 8 | 2 | no | — |
| 162 | 2−1+4 | — | 3 | 2 | no | — |
| 163 | 2−1+4 | C2×C3×D3 | 1 | 2 | yes | — |
| 164 | #137 | — | 3 | 2 | no | — |
| 165 | #137 | — | 3 | 2 | no | — |
| 166 | #137 | — | 3 | 2 | no | — |
| 167 | #137 | — | 3 | 2 | no | — |
| 168 | #137 | — | 6 | 2 | no | — |
| 169 | #137 | — | 6 | 2 | no | — |
| 170 | #137 | — | 6 | 2 | no | — |
| 171 | #135 | — | 3 | 1 | no | — |
| 172 | #135 | — | 3 | 1 | no | — |
| 173 | #135 | — | 6 | 2 | no | — |
| 174 | #135 | — | 6 | 1 | no | — |
| 175 | C2×Q16 | — | 3 | 1 | no | — |
| 176 | C2×Q16 | — | 3 | 2 | no | — |
| 177 | C2×Q16 | — | 3 | 1 | no | — |
| 178 | C2×Q16 | — | 6 | 2 | no | — |
| 179 | C2×Q16 | — | 6 | 1 | no | — |
| 180 | #131 | — | 3 | 2 | no | — |
| 181 | #131 | — | 3 | 1 | no | — |
| 182 | #131 | C2×C3×D3 | 1 | 1 | yes | characteristic |
| 183 | C4⋊Q8 | — | 3 | 2 | no | — |
| 184 | #108 | — | 3 | 1 | no | — |
| 185 | #108 | — | 3 | 1 | no | — |
| 186 | #104 | — | 3 | 1 | no | — |
| 187 | #104 | — | 3 | 2 | no | — |
| 188 | #104 | — | 3 | 1 | no | — |
| 189 | #101 | — | 3 | 2 | no | — |
| 190 | #101 | — | 3 | 2 | no | — |
| 191 | C4×C8 | — | 3 | 1 | no | — |
| 192 | C3×Q8 | — | 3 | 1 | no | — |
| 193 | C3×Q8 | — | 3 | 2 | no | — |
| 194 | C3×Q8 | — | 6 | 2 | no | — |
| 195 | C3×Q8 | — | 6 | 2 | no | — |
| 196 | C3×Q8 | — | 6 | 2 | no | — |
| 197 | C3×Q8 | — | 12 | 2 | no | — |
| 198 | C3×Q8 | D3×D4 | 1 | 1 | yes | characteristic |
| 199 | C3×D4 | — | 3 | 1 | no | — |
| 200 | C3×D4 | — | 3 | 1 | no | — |
| 201 | C3×D4 | — | 4 | 2 | no | — |
| 202 | C3×D4 | — | 6 | 2 | no | — |
| 203 | C3×D4 | — | 6 | 1 | no | — |
| 204 | C3×D4 | — | 8 | 2 | no | — |
| 205 | C3×D4 | — | 12 | 2 | no | — |
| 206 | C3×D4 | C2×S4 | 1 | 2 | yes | — |
| 207 | C2×C3×C4 | — | 3 | 1 | no | — |
| 208 | C2×C3×C4 | — | 6 | 2 | no | — |
| 209 | C2×C3×C4 | — | 6 | 1 | no | — |
| 210 | C2×C3×C4 | — | 6 | 1 | no | — |
| 211 | C2×C3×C4 | — | 6 | 2 | no | — |
| 212 | C2×C3×C4 | — | 6 | 2 | no | — |
| 213 | C2×C3×C4 | — | 12 | 2 | no | — |
| 214 | C2×C3×C4 | — | 12 | 2 | no | — |
| 215 | #67 | — | 8 | 2 | no | — |
| 216 | C2×Dic3 | — | 8 | 2 | no | — |
| 217 | C4×D3 | — | 4 | 1 | no | — |
| 218 | Dic6 | — | 4 | 2 | no | — |
| 219 | SL(2,𝔽3) | — | 2 | 1 | no | — |
| 220 | SL(2,𝔽3) | C2×C3×D4 | 1 | 1 | yes | characteristic |
| 221 | C3×C8 | — | 3 | 1 | no | — |
| 222 | C3×C8 | — | 3 | 1 | no | — |
| 223 | C3×C8 | — | 3 | 1 | no | — |
| 224 | C3×C8 | — | 4 | 1 | no | — |
| 225 | C3×C8 | — | 6 | 2 | no | — |
| 226 | C3×C8 | — | 6 | 1 | no | — |
| 227 | C3×C8 | — | 8 | 1 | no | — |
| 228 | C3×C8 | C2×S4 | 1 | 1 | yes | characteristic |
| 229 | C3⋊C8 | — | 4 | 1 | no | — |
| 230 | C2×C32 | — | 4 | 1 | no | — |
| 231 | C2×C32 | — | 16 | 2 | no | — |
| 232 | C3×D3 | — | 8 | 1 | no | — |
| 233 | #41 | — | 3 | 1 | no | — |
| 234 | #41 | — | 3 | 2 | no | — |
| 235 | #41 | — | 6 | 2 | no | — |
| 236 | #41 | — | 6 | 2 | no | — |
| 237 | #41 | — | 6 | 2 | no | — |
| 238 | #41 | — | 12 | 2 | no | — |
| 239 | #41 | C22×C3×D3 | 1 | 1 | yes | characteristic |
| 240 | C2×Q8 | — | 2 | 2 | no | — |
| 241 | C2×Q8 | — | 3 | 2 | no | — |
| 242 | C2×Q8 | — | 3 | 2 | no | — |
| 243 | C2×Q8 | — | 6 | 2 | no | — |
| 244 | C2×Q8 | — | 6 | 2 | no | — |
| 245 | Q16 | — | 3 | 1 | no | — |
| 246 | Q16 | — | 3 | 1 | no | — |
| 247 | Q16 | — | 6 | 1 | no | — |
| 248 | Q16 | — | 6 | 2 | no | — |
| 249 | Q16 | — | 6 | 2 | no | — |
| 250 | Q16 | — | 6 | 1 | no | — |
| 251 | Q16 | — | 6 | 2 | no | — |
| 252 | Q16 | — | 6 | 2 | no | — |
| 253 | Q16 | — | 6 | 2 | no | — |
| 254 | Q16 | — | 6 | 1 | no | — |
| 255 | SD16 | — | 3 | 1 | no | — |
| 256 | SD16 | — | 3 | 1 | no | — |
| 257 | SD16 | — | 3 | 2 | no | — |
| 258 | SD16 | — | 6 | 2 | no | — |
| 259 | SD16 | — | 6 | 2 | no | — |
| 260 | SD16 | — | 6 | 2 | no | — |
| 261 | D8 | — | 3 | 1 | no | — |
| 262 | D8 | C3×S4 | 1 | 1 | yes | characteristic |
| 263 | M16 | — | 3 | 1 | no | — |
| 264 | M16 | — | 3 | 2 | no | — |
| 265 | M16 | — | 3 | 1 | no | — |
| 266 | M16 | — | 6 | 2 | no | — |
| 267 | M16 | — | 6 | 1 | no | — |
| 268 | C2×C8 | — | 3 | 1 | no | — |
| 269 | C2×C8 | — | 3 | 1 | no | — |
| 270 | C2×C8 | — | 6 | 2 | no | — |
| 271 | C2×C8 | — | 6 | 1 | no | — |
| 272 | C4⋊C4 | — | 12 | 2 | no | — |
| 273 | C42 | — | 3 | 1 | no | — |
| 274 | C22×C3 | — | 2 | 2 | no | — |
| 275 | C22×C3 | — | 3 | 1 | no | — |
| 276 | C22×C3 | — | 6 | 1 | no | — |
| 277 | C22×C3 | — | 8 | 2 | no | — |
| 278 | C22×C3 | — | 16 | 2 | no | — |
| 279 | C2×D3 | — | 4 | 1 | no | — |
| 280 | C3×C4 | — | 3 | 1 | no | — |
| 281 | C3×C4 | — | 4 | 1 | no | — |
| 282 | C3×C4 | — | 6 | 2 | no | — |
| 283 | C3×C4 | — | 6 | 2 | no | — |
| 284 | C3×C4 | — | 6 | 1 | no | — |
| 285 | C3×C4 | — | 8 | 1 | no | — |
| 286 | C3×C4 | — | 12 | 2 | no | — |
| 287 | C3×C4 | C22×S4 | 1 | 1 | yes | characteristic |
| 288 | Dic3 | — | 4 | 1 | no | — |
| 289 | Dic3 | — | 8 | 2 | no | — |
| 290 | C32 | — | 4 | 1 | no | Sylow |
| 291 | Q8 | — | 3 | 1 | no | — |
| 292 | Q8 | — | 3 | 2 | no | — |
| 293 | Q8 | — | 6 | 2 | no | — |
| 294 | Q8 | — | 6 | 2 | no | — |
| 295 | Q8 | — | 6 | 2 | no | — |
| 296 | Q8 | — | 12 | 2 | no | — |
| 297 | Q8 | C3×D3×D4 | 1 | 1 | yes | characteristic |
| 298 | D4 | — | 3 | 1 | no | — |
| 299 | D4 | — | 3 | 1 | no | — |
| 300 | D4 | — | 6 | 2 | no | — |
| 301 | D4 | — | 6 | 1 | no | — |
| 302 | D4 | — | 12 | 2 | no | — |
| 303 | D4 | C2×C3×S4 | 1 | 2 | yes | — |
| 304 | C2×C4 | — | 3 | 1 | no | — |
| 305 | C2×C4 | — | 6 | 2 | no | — |
| 306 | C2×C4 | — | 6 | 1 | no | — |
| 307 | C2×C4 | — | 6 | 1 | no | — |
| 308 | C2×C4 | — | 6 | 2 | no | — |
| 309 | C2×C4 | — | 6 | 2 | no | — |
| 310 | C2×C4 | — | 12 | 2 | no | — |
| 311 | C2×C4 | — | 12 | 2 | no | — |
| 312 | C8 | — | 3 | 1 | no | — |
| 313 | C8 | — | 3 | 1 | no | — |
| 314 | C8 | — | 3 | 1 | no | — |
| 315 | C8 | — | 6 | 2 | no | — |
| 316 | C8 | — | 6 | 1 | no | — |
| 317 | C8 | C2×C3×S4 | 1 | 1 | yes | characteristic |
| 318 | C2×C3 | — | 4 | 2 | no | — |
| 319 | C2×C3 | — | 4 | 1 | no | — |
| 320 | C2×C3 | — | 6 | 1 | no | — |
| 321 | C2×C3 | — | 8 | 1 | no | — |
| 322 | C2×C3 | — | 12 | 1 | no | — |
| 323 | C2×C3 | — | 16 | 2 | no | — |
| 324 | C2×C3 | — | 32 | 2 | no | — |
| 325 | C2×C3 | D4×S4 | 1 | 1 | yes | characteristic |
| 326 | D3 | — | 8 | 1 | no | — |
| 327 | C22 | — | 2 | 2 | no | — |
| 328 | C22 | — | 3 | 1 | no | — |
| 329 | C22 | — | 6 | 1 | no | — |
| 330 | C4 | — | 3 | 1 | no | — |
| 331 | C4 | — | 6 | 2 | no | — |
| 332 | C4 | — | 6 | 2 | no | — |
| 333 | C4 | — | 6 | 1 | no | — |
| 334 | C4 | — | 12 | 2 | no | — |
| 335 | C4 | C22×C3×S4 | 1 | 1 | yes | characteristic |
| 336 | C3 | — | 4 | 1 | no | — |
| 337 | C3 | — | 8 | 1 | no | — |
| 338 | C3 | #85475 | 1 | 1 | yes | characteristic, direct product factor |
| 339 | C2 | — | 4 | 2 | no | — |
| 340 | C2 | — | 6 | 1 | no | — |
| 341 | C2 | — | 12 | 1 | no | — |
| 342 | C2 | C3×D4×S4 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C3 | D4×S4 |
| commutator, cosocle | #41⋊C3 | C23×C3 |
| Frattini | C4 | C22×C3×S4 |
| Fitting | C3×#578 | D3 |
| hypercenter | C3×D8 | S4 |
| hypocenter | SL(2,𝔽3) | C2×C3×D4 |
| LCS | G ▷ #41⋊C3 ▷ SL(2,𝔽3) | |
| UCS | C1 ◁ C2×C3 ◁ C3×C4 ◁ C3×D8 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C3×#5927 | C2 | semidirect |
| 2. C3×#578⋊C3 | C2 | semidirect |
| 3. C3×#5430 | C2 | semidirect |
| 4. C3×#5404 | C2 | semidirect |
| 5. C3×#5403 | C2 | semidirect |
| 6. #85475 | C3 | direct (N × H) |
| 16. #5927 | C2×C3 | semidirect |
| 19. C3×#578 | D3 | semidirect |
| 21. #578⋊C3 | C2×C3 | semidirect |
| 22. #5430 | C2×C3 | semidirect |
| 23. #5404 | C2×C3 | semidirect |
| 24. #5403 | C2×C3 | semidirect |
| 94. #578 | C3×D3 | semidirect |
| 338. C3 | #85475 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#5927 | 2 |
| C3×#578⋊C3 | 2 |
| C3×#5430 | 2 |
| C3×#5404 | 2 |
| C3×#5403 | 2 |
| #85475 | 3 |
| C3×#3293 | 3 |
| C3×#912 | 4 |