Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
562 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 562 conjugacy classes of subgroups — too many to draw. Only its 113 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×#88525 | C2 | semidirect |
| 2. C2×C3×D72 | C2 | semidirect |
| 3. #11721006 | C2 | semidirect |
| 4. C2×#88417 | C2 | semidirect |
| 5. C8×C9×Dic3 | C2 | semidirect |
| 25. C2×D72 | D3 | semidirect |
| 37. C3×C8×C9 | D4 | semidirect |
| 38. C9×C3⋊C8 | D4 | semidirect |
| 69. C9×Dic3 | D8 | semidirect |
| 80. C8×Dic3 | D9 | semidirect |
| 107. C8×C9 | #67 | semidirect |
| 160. C3×C9 | #493 | semidirect |
| 185. C3×C8 | D36 | semidirect |
| 187. C3⋊C8 | D36 | semidirect |
| 228. Dic3 | D72 | semidirect |
| 231. C9 | #5151 | semidirect |
| 242. C8 | #6192 | semidirect |
| 263. C3 | #10588377 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#88525 | 2 |
| C2×C3×D72 | 2 |
| #11721006 | 2 |
| C2×#88417 | 2 |
| C8×C9×Dic3 | 2 |
| #10590880 | 3 |
| #10588377 | 3 |