Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
550 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 550 conjugacy classes of subgroups — too many to draw. Only its 85 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. C3×#63710 | C2 | semidirect |
| 2. C9×#940 | C2 | semidirect |
| 3. #11720883 | C2 | semidirect |
| 4. #11720575 | C2 | semidirect |
| 5. #11720260 | C2 | semidirect |
| 13. C2×C9×D12 | C22 | semidirect |
| 15. #88532 | C22 | semidirect |
| 16. C4×C9×Dic3 | C22 | semidirect |
| 22. #63710 | D3 | semidirect |
| 41. C3×D36 | D4 | semidirect |
| 43. C3×Dic18 | D4 | semidirect |
| 85. #940 | D9 | semidirect |
| 121. D36 | #67 | semidirect |
| 123. Dic18 | #67 | semidirect |
| 146. C2×D12 | C2×D9 | semidirect |
| 152. C4×Dic3 | C2×D9 | semidirect |
| 185. C3×C9 | #453 | semidirect |
| 270. C9 | #5241 | semidirect |
| 310. C3 | #10588757 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#63710 | 2 |
| C9×#940 | 2 |
| #11720883 | 2 |
| #11720575 | 2 |
| #11720260 | 2 |
| #10591509 | 3 |
| #10588757 | 3 |