Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
536 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 536 conjugacy classes of subgroups — too many to draw. Only its 89 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×#88642 | C2 | semidirect |
| 2. C9×#895 | C2 | semidirect |
| 3. C2×#88423 | C2 | semidirect |
| 4. C2×#88422 | C2 | semidirect |
| 5. #11720528 | C2 | semidirect |
| 6. C3×#63368 | C2 | semidirect |
| 7. (C2×D3)⋊(C9⋊C8) | C2 | semidirect |
| 39. #63368 | D3 | semidirect |
| 46. C4⋊(C3⋊D9) | D4 | semidirect |
| 55. C3×Dic18 | D4 | semidirect |
| 117. #895 | D9 | semidirect |
| 167. Dic18 | D12 | semidirect |
| 255. C3×C9 | #449 | semidirect |
| 372. C9 | #4810 | semidirect |
| 425. C3 | #10588720 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#88642 | 2 |
| C9×#895 | 2 |
| C2×#88423 | 2 |
| C2×#88422 | 2 |
| #11720528 | 2 |
| C3×#63368 | 2 |
| (C2×D3)⋊(C9⋊C8) | 2 |
| #10590615 | 3 |
| #10588720 | 3 |