Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
322 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 322 conjugacy classes of subgroups — too many to draw. Only its 72 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. C2×#3744 | C2 | semidirect |
| 2. C2×C3×D24 | C2 | semidirect |
| 3. #63911 | C2 | semidirect |
| 4. #63860 | C2 | semidirect |
| 5. C2×#3716 | C2 | semidirect |
| 6. C2×#3714 | C2 | semidirect |
| 7. C3×#815 | C2 | semidirect |
| 29. C2×D24 | D3 | semidirect |
| 37. #815 | D3 | semidirect |
| 53. C32×C8 | D4 | semidirect |
| 54. C3×C3⋊C8 | D4 | semidirect |
| 143. C3×C8 | D12 | semidirect |
| 144. C3×C8 | #67 | semidirect |
| 145. C3⋊C8 | D12 | semidirect |
| 192. C32 | #496 | semidirect |
| 209. C8 | #626 | semidirect |
| 235. C3 | #4712 | semidirect |
| 236. C3 | #5154 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#3744 | 2 |
| C2×C3×D24 | 2 |
| #63911 | 2 |
| #63860 | 2 |
| C2×#3716 | 2 |
| C2×#3714 | 2 |
| C3×#815 | 2 |
| #5154 | 3 |
| #4712 | 3 |