Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
374 conjugacy classes of subgroups; only the 112 normal subgroups are shown.
This group has 374 conjugacy classes of subgroups — too many to draw. Only its 112 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. C2×C3×C4×Dic3 | C2 | semidirect |
| 4. #63569 | C2 | direct (N × H) |
| 12. C3×#235 | C4 | semidirect |
| 14. C2×C3×D12 | C4 | semidirect |
| 16. C2×C3×Dic6 | C4 | semidirect |
| 18. #3748 | C22 | semidirect |
| 21. C3×C4×Dic3 | C22 | semidirect |
| 25. C2×C4×Dic3 | D3 | semidirect |
| 45. C3×D12 | C2×C4 | semidirect |
| 49. C3×Dic6 | C2×C4 | semidirect |
| 68. #235 | Dic3 | semidirect |
| 70. C2×D12 | Dic3 | semidirect |
| 72. C2×Dic6 | Dic3 | semidirect |
| 76. C4×Dic3 | C2×D3 | semidirect |
| 142. D12 | C2×Dic3 | semidirect |
| 146. Dic6 | C2×Dic3 | semidirect |
| 152. C2×C32 | #104 | semidirect |
| 202. C32 | C2×#104 | semidirect |
| 232. C2×C3 | #805 | semidirect |
| 233. C2×C3 | #837 | semidirect |
| 250. C3 | C2×#805 | semidirect |
| 251. C3 | C2×#837 | semidirect |
| 255. C2 | #63569 | direct (N × H) |
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 |
| C2×C3×C4×Dic3 | 2 |
| #63569 | 2 |
| C2×#837 | 3 |
| C2×#805 | 3 |