Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
738 conjugacy classes of subgroups; only the 192 normal subgroups are shown.
This group has 738 conjugacy classes of subgroups — too many to draw. Only its 192 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. C22×#634 | C2 | semidirect |
| 3. C2×C3×C4×Dic3 | C2 | semidirect |
| 4. C2×(C2×D3)⋊Dic3 | C2 | semidirect |
| 5. #63860 | C2 | direct (N × H) |
| 12. C2×#634 | C22 | semidirect |
| 16. C3×C4×Dic3 | C22 | semidirect |
| 17. (C2×D3)⋊Dic3 | C22 | semidirect |
| 27. C2×C4×Dic3 | D3 | semidirect |
| 65. C4×Dic3 | C2×D3 | semidirect |
| 110. C2×C32 | #124 | semidirect |
| 147. C32 | C2×#124 | semidirect |
| 164. C2×C3 | #875 | semidirect |
| 165. C2×C3 | #936 | semidirect |
| 181. C3 | C2×#875 | semidirect |
| 182. C3 | C2×#936 | semidirect |
| 184. C2 | #63860 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#634 | 2 |
| C22×C3×D12 | 2 |
| C2×C3×C4×Dic3 | 2 |
| C2×(C2×D3)⋊Dic3 | 2 |
| #63860 | 2 |
| C2×#936 | 3 |
| C2×#875 | 3 |