Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
1836 conjugacy classes of subgroups; only the 276 normal subgroups are shown.
This group has 1836 conjugacy classes of subgroups — too many to draw. Only its 276 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 |
|---|---|---|
| 1. C2×#89014 | C2 | semidirect |
| 2. C2×#88853 | C2 | semidirect |
| 3. C2×C3×C8×C3⋊D3 | C2 | semidirect |
| 4. C2×C32×D24 | C2 | semidirect |
| 5. C2×#88794 | C2 | semidirect |
| 6. #11723339 | C2 | direct (N × H) |
| 15. #89014 | C22 | semidirect |
| 17. #88853 | C22 | semidirect |
| 19. C3×C8×C3⋊D3 | C22 | semidirect |
| 20. C32×D24 | C22 | semidirect |
| 21. #88794 | C22 | semidirect |
| 30. C2×C8×C3⋊D3 | D3 | semidirect |
| 31. C2×C3×D24 | D3 | semidirect |
| 76. C8×C3⋊D3 | C2×D3 | semidirect |
| 78. C3×D24 | C2×D3 | semidirect |
| 100. C2×D24 | C3⋊D3 | semidirect |
| 139. C2×C33 | #135 | semidirect |
| 169. D24 | C2×C3⋊D3 | semidirect |
| 200. C33 | C2×#135 | semidirect |
| 239. C2×C32 | #904 | semidirect |
| 240. C2×C32 | #912 | semidirect |
| 282. C32 | C2×#904 | semidirect |
| 283. C32 | C2×#912 | semidirect |
| 303. C2×C3 | #63807 | semidirect |
| 304. C2×C3 | #64121 | semidirect |
| 319. C3 | C2×#63807 | semidirect |
| 320. C3 | C2×#64121 | semidirect |
| 323. C2 | #11723339 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#89014 | 2 |
| C2×#88853 | 2 |
| C2×C3×C8×C3⋊D3 | 2 |
| C2×C32×D24 | 2 |
| C2×#88794 | 2 |
| #11723339 | 2 |
| C2×#64121 | 3 |
| C2×#63807 | 3 |