Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
438 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 438 conjugacy classes of subgroups — too many to draw. Only its 105 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. C9×#893 | C2 | semidirect |
| 2. Dic3×D36 | C2 | semidirect |
| 4. #11720525 | C2 | semidirect |
| 5. C3×#63369 | C2 | semidirect |
| 6. #11720295 | C2 | semidirect |
| 7. Dic3×C9⋊C8 | C2 | semidirect |
| 21. #88421 | C4 | semidirect |
| 33. #63369 | D3 | semidirect |
| 45. C9×D12 | C2×C4 | semidirect |
| 48. C3×D36 | C2×C4 | semidirect |
| 50. C3⋊(C9⋊C8) | C2×C4 | semidirect |
| 93. C9×Dic3 | D8 | semidirect |
| 98. #893 | D9 | semidirect |
| 138. D36 | C4×D3 | semidirect |
| 214. C3×C9 | C4×D8 | semidirect |
| 241. D12 | C4×D9 | semidirect |
| 304. Dic3 | #3673 | semidirect |
| 307. C9 | #4756 | semidirect |
| 350. C3 | C4×#3673 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C9×#893 | 2 |
| Dic3×D36 | 2 |
| C2×#88421 | 2 |
| #11720525 | 2 |
| C3×#63369 | 2 |
| #11720295 | 2 |
| Dic3×C9⋊C8 | 2 |
| #10590452 | 3 |
| C4×#3673 | 3 |