Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
266 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 266 conjugacy classes of subgroups — too many to draw. Only its 86 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. C3×C4×Dic6 | C2 | semidirect |
| 4. C4×C3⋊(C3⋊C8) | C2 | semidirect |
| 5. #63574 | C2 | semidirect |
| 6. #63565 | C2 | semidirect |
| 21. #3715 | C4 | direct (N × H) |
| 27. C4×Dic6 | D3 | semidirect |
| 48. C3×Dic6 | C2×C4 | semidirect |
| 50. C3⋊(C3⋊C8) | C2×C4 | semidirect |
| 84. C32×C4 | SD16 | semidirect |
| 123. Dic6 | C4×D3 | semidirect |
| 164. C3×C4 | #214 | semidirect |
| 165. C3×C4 | #215 | semidirect |
| 173. C32 | C4×SD16 | semidirect |
| 207. C4 | #3715 | direct (N × H) |
| 211. C3 | C4×#214 | semidirect |
| 212. C3 | C4×#215 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C4×D12 | 2 |
| C3×C4×Dic6 | 2 |
| C2×#3715 | 2 |
| C4×C3⋊(C3⋊C8) | 2 |
| #63574 | 2 |
| #63565 | 2 |
| #63562 | 2 |
| C4×#215 | 3 |
| C4×#214 | 3 |