Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
345 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 345 conjugacy classes of subgroups — too many to draw. Only its 66 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×#3795 | C2 | semidirect |
| 2. C2×C3×D24 | C2 | semidirect |
| 3. #63908 | C2 | semidirect |
| 4. C2×#3716 | C2 | semidirect |
| 5. #63643 | C2 | semidirect |
| 6. C3×(C2×D3)⋊C8 | C2 | semidirect |
| 7. #63563 | C2 | semidirect |
| 31. C2×D24 | D3 | semidirect |
| 36. (C2×D3)⋊C8 | D3 | semidirect |
| 47. #634 | D4 | semidirect |
| 52. C3×D12 | D4 | semidirect |
| 147. D12 | #67 | semidirect |
| 218. C32 | #449 | semidirect |
| 270. C3 | #4734 | semidirect |
| 271. C3 | #5158 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#3795 | 2 |
| C2×C3×D24 | 2 |
| #63908 | 2 |
| C2×#3716 | 2 |
| #63643 | 2 |
| C3×(C2×D3)⋊C8 | 2 |
| #63563 | 2 |
| #5158 | 3 |
| #4734 | 3 |