Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
414 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 414 conjugacy classes of subgroups — too many to draw. Only its 87 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×#63509 | C2 | semidirect |
| 2. C2×C9×#215 | C2 | semidirect |
| 3. D12×Dic9 | C2 | semidirect |
| 5. #11720582 | C2 | semidirect |
| 6. #11720283 | C2 | semidirect |
| 7. Dic9⋊(C3⋊C8) | C2 | semidirect |
| 31. #63509 | D3 | semidirect |
| 101. C2×#215 | D9 | semidirect |
| 224. C3×C9 | #463 | semidirect |
| 322. C9 | #5057 | semidirect |
| 366. C3 | #10588845 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#63509 | 2 |
| C2×C9×#215 | 2 |
| D12×Dic9 | 2 |
| C2×#88421 | 2 |
| #11720582 | 2 |
| #11720283 | 2 |
| Dic9⋊(C3⋊C8) | 2 |
| #10591567 | 3 |
| #10588845 | 3 |