Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
448 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 448 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. #11721712 | C2 | semidirect |
| 2. C4×C9×D12 | C2 | semidirect |
| 3. C2×#88424 | C2 | semidirect |
| 5. C3×C4⋊(C9⋊C8) | C2 | semidirect |
| 6. #11720269 | C2 | semidirect |
| 7. #11720267 | C2 | semidirect |
| 37. C4⋊(C9⋊C8) | D3 | semidirect |
| 108. C4×D12 | D9 | semidirect |
| 235. C3×C9 | #463 | semidirect |
| 341. C9 | #4844 | semidirect |
| 386. C3 | #10588699 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11721712 | 2 |
| C4×C9×D12 | 2 |
| C2×#88424 | 2 |
| C2×#88422 | 2 |
| C3×C4⋊(C9⋊C8) | 2 |
| #11720269 | 2 |
| #11720267 | 2 |
| #10590366 | 3 |
| #10588699 | 3 |