Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
2172 conjugacy classes of subgroups; only the 452 normal subgroups are shown.
This group has 2172 conjugacy classes of subgroups — too many to draw. Only its 452 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 4. C2×#88800 | C2 | direct (N × H) |
| 15. #88800 | C22 | direct (N × H) |
| 59. C22×C33 | Q16 | semidirect |
| 101. C2×C33 | C2×Q16 | semidirect |
| 127. C22×C32 | Dic12 | semidirect |
| 128. C22×C32 | #216 | semidirect |
| 146. C33 | C22×Q16 | semidirect |
| 175. C2×C32 | C2×Dic12 | semidirect |
| 176. C2×C32 | C2×#216 | semidirect |
| 190. C22×C3 | #3719 | semidirect |
| 191. C22×C3 | #3746 | semidirect |
| 206. C32 | C22×Dic12 | semidirect |
| 207. C32 | C22×#216 | semidirect |
| 220. C2×C3 | C2×#3719 | semidirect |
| 221. C2×C3 | C2×#3746 | semidirect |
| 224. C22 | #88800 | direct (N × H) |
| 231. C3 | C22×#3719 | semidirect |
| 232. C3 | C22×#3746 | semidirect |
| 233. C2 | C2×#88800 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#6308 | 2 |
| C22×C3×#634 | 2 |
| C22×C32×C3⋊C8 | 2 |
| C2×#88800 | 2 |
| C22×#3746 | 3 |
| C22×#3719 | 3 |