Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
572 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 572 conjugacy classes of subgroups — too many to draw. Only its 81 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 |
|---|---|---|
| 2. C3×#63511 | C2 | semidirect |
| 3. #11720932 | C2 | semidirect |
| 4. #11720871 | C2 | semidirect |
| 5. C9×#837 | C2 | semidirect |
| 6. #11720290 | C2 | semidirect |
| 7. #11720261 | C2 | semidirect |
| 36. #63511 | D3 | semidirect |
| 128. #837 | D9 | semidirect |
| 275. C3×C9 | #456 | semidirect |
| 395. C9 | #5205 | semidirect |
| 441. C3 | #10588506 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11722673 | 2 |
| C3×#63511 | 2 |
| #11720932 | 2 |
| #11720871 | 2 |
| C9×#837 | 2 |
| #11720290 | 2 |
| #11720261 | 2 |
| #10591668 | 3 |
| #10588506 | 3 |