Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
438 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 438 conjugacy classes of subgroups — too many to draw. Only its 117 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 |
|---|---|---|
| 2. Dic3×D36 | C2 | semidirect |
| 3. #11720541 | C2 | semidirect |
| 4. C8×C9×Dic3 | C2 | semidirect |
| 5. #11720283 | C2 | semidirect |
| 14. C3×D72 | C4 | semidirect |
| 33. C3×D36 | C2×C4 | semidirect |
| 35. C3×C8×C9 | C2×C4 | semidirect |
| 56. D72 | Dic3 | direct (N × H) |
| 65. C9×Dic3 | D8 | semidirect |
| 76. C8×Dic3 | D9 | semidirect |
| 95. D36 | C2×Dic3 | semidirect |
| 99. C8×C9 | C2×Dic3 | semidirect |
| 150. C3×C9 | C4×D8 | semidirect |
| 171. C3×C8 | C4×D9 | semidirect |
| 214. Dic3 | D72 | direct (N × H) |
| 217. C9 | Dic3×D8 | semidirect |
| 227. C8 | Dic3×D9 | semidirect |
| 249. C3 | C4×D72 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×D72 | 2 |
| Dic3×D36 | 2 |
| #11720541 | 2 |
| C8×C9×Dic3 | 2 |
| #11720283 | 2 |
| Dic3×D24 | 3 |
| C4×D72 | 3 |