Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
478 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 478 conjugacy classes of subgroups — too many to draw. Only its 109 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. #11720993 | C2 | semidirect |
| 3. C8×C9×Dic3 | C2 | semidirect |
| 4. C3×#63378 | C2 | semidirect |
| 5. #11720284 | C2 | semidirect |
| 11. #88525 | C4 | semidirect |
| 26. #63378 | D3 | semidirect |
| 30. C4⋊(C3⋊D9) | C2×C4 | semidirect |
| 35. C3×C8×C9 | C2×C4 | semidirect |
| 65. C9×Dic3 | D8 | semidirect |
| 76. C8×Dic3 | D9 | semidirect |
| 102. C8×C9 | C4×D3 | semidirect |
| 156. C3×C9 | C4×D8 | semidirect |
| 179. C3×C8 | C4×D9 | semidirect |
| 225. Dic3 | D72 | semidirect |
| 228. C9 | #4872 | semidirect |
| 238. C8 | (C3⋊D9)⋊C4 | semidirect |
| 261. C3 | C4×D72 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#88525 | 2 |
| #11720993 | 2 |
| C8×C9×Dic3 | 2 |
| C3×#63378 | 2 |
| #11720284 | 2 |
| #10590763 | 3 |
| C4×D72 | 3 |