Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
470 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 470 conjugacy classes of subgroups — too many to draw. Only its 91 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×#63502 | C2 | semidirect |
| 2. C2×C9×#213 | C2 | semidirect |
| 3. D12×Dic9 | C2 | semidirect |
| 4. C2×#88421 | C2 | semidirect |
| 5. #11720576 | C2 | semidirect |
| 6. #11720283 | C2 | semidirect |
| 7. Dic9⋊(C3⋊C8) | C2 | semidirect |
| 31. #63502 | D3 | semidirect |
| 50. C9×D12 | D4 | semidirect |
| 101. C3×Dic9 | D8 | semidirect |
| 108. C2×#213 | D9 | semidirect |
| 231. Dic9 | #213 | semidirect |
| 239. C3×C9 | #459 | semidirect |
| 275. D12 | #611 | semidirect |
| 350. C9 | #5072 | semidirect |
| 401. C3 | #10588830 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#63502 | 2 |
| C2×C9×#213 | 2 |
| D12×Dic9 | 2 |
| C2×#88421 | 2 |
| #11720576 | 2 |
| #11720283 | 2 |
| Dic9⋊(C3⋊C8) | 2 |
| #10591428 | 3 |
| #10588830 | 3 |