Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
516 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 516 conjugacy classes of subgroups — too many to draw. Only its 95 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×D3×Dic18 | C2 | semidirect |
| 3. C2×#88424 | C2 | semidirect |
| 4. C2×#88423 | C2 | semidirect |
| 5. #11720527 | C2 | semidirect |
| 6. C3×#63368 | C2 | semidirect |
| 7. (C2×D3)⋊(C9⋊C8) | C2 | semidirect |
| 39. #63368 | D3 | semidirect |
| 46. #6226 | D4 | semidirect |
| 55. C3×Dic18 | D4 | semidirect |
| 101. C2×D3×C9 | SD16 | semidirect |
| 165. Dic18 | D12 | semidirect |
| 246. C3×C9 | #448 | semidirect |
| 335. C2×D3 | #3672 | semidirect |
| 354. C9 | #4806 | semidirect |
| 402. C3 | #10588716 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D3×Dic18 | 2 |
| C9×#895 | 2 |
| C2×#88424 | 2 |
| C2×#88423 | 2 |
| #11720527 | 2 |
| C3×#63368 | 2 |
| (C2×D3)⋊(C9⋊C8) | 2 |
| #10590603 | 3 |
| #10588716 | 3 |