Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
438 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 438 conjugacy classes of subgroups — too many to draw. Only its 101 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. C2×D3×C8×C9 | C2 | semidirect |
| 2. C2×C3×D72 | C2 | semidirect |
| 3. #11721037 | C2 | semidirect |
| 4. #11720541 | C2 | semidirect |
| 5. #11720283 | C2 | semidirect |
| 24. C2×D72 | D3 | semidirect |
| 38. C3×C8×C9 | D4 | semidirect |
| 65. C2×D3×C9 | D8 | semidirect |
| 78. C2×D3×C8 | D9 | semidirect |
| 110. C8×C9 | #67 | semidirect |
| 168. C3×C9 | #466 | semidirect |
| 193. C3×C8 | #611 | semidirect |
| 232. C2×D3 | D72 | semidirect |
| 246. C9 | #5157 | semidirect |
| 258. C8 | #6194 | semidirect |
| 284. C3 | #10588796 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D3×C8×C9 | 2 |
| C2×C3×D72 | 2 |
| #11721037 | 2 |
| #11720541 | 2 |
| #11720283 | 2 |
| #10590831 | 3 |
| #10588796 | 3 |