Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
342 conjugacy classes of subgroups; only the 104 normal subgroups are shown.
This group has 342 conjugacy classes of subgroups — too many to draw. Only its 104 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. C2×#3748 | C2 | semidirect |
| 3. C3×#926 | C2 | semidirect |
| 4. #63569 | C2 | semidirect |
| 11. C3×#235 | C4 | semidirect |
| 13. C2×C3×D12 | C4 | semidirect |
| 15. C2×C3×Dic6 | C4 | semidirect |
| 17. #3748 | C22 | semidirect |
| 21. C3×C4×Dic3 | C22 | semidirect |
| 25. #926 | D3 | semidirect |
| 65. #235 | Dic3 | semidirect |
| 67. C2×D12 | Dic3 | semidirect |
| 69. C2×Dic6 | Dic3 | semidirect |
| 75. C4×Dic3 | C2×D3 | semidirect |
| 199. C32 | #421 | semidirect |
| 246. C3 | #5005 | semidirect |
| 247. C3 | #5236 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×#235 | 2 |
| C2×#3748 | 2 |
| C3×#926 | 2 |
| #63569 | 2 |
| #5236 | 3 |
| #5005 | 3 |