Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
420 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 420 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. #11721805 | C2 | semidirect |
| 2. C3×C9×Q32 | C2 | semidirect |
| 3. #11720567 | C2 | semidirect |
| 4. #11720507 | C2 | semidirect |
| 5. C16×C3⋊D9 | C2 | semidirect |
| 21. C9×Q32 | D3 | semidirect |
| 55. C3×Q32 | D9 | semidirect |
| 106. Q32 | C3⋊D9 | semidirect |
| 110. C3×C9 | #508 | semidirect |
| 149. C9 | #4919 | semidirect |
| 168. C3 | #10588599 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11721805 | 2 |
| C3×C9×Q32 | 2 |
| #11720567 | 2 |
| #11720507 | 2 |
| C16×C3⋊D9 | 2 |
| #10592618 | 3 |
| #10588599 | 3 |