Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
418 conjugacy classes of subgroups; only the 112 normal subgroups are shown.
This group has 418 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. #64135 | C2 | semidirect |
| 3. C2×C3×#208 | C2 | semidirect |
| 4. #63563 | C2 | semidirect |
| 11. C2×C3×D12 | C4 | semidirect |
| 14. C4⋊(C3⋊Dic3) | C22 | semidirect |
| 17. C2×C3×C3⋊C8 | C22 | semidirect |
| 24. C2×#208 | D3 | semidirect |
| 52. C2×D12 | Dic3 | semidirect |
| 66. C2×C3⋊C8 | C2×D3 | semidirect |
| 155. C32 | #418 | semidirect |
| 191. C3 | #5131 | semidirect |
| 192. C3 | #5215 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C3×D12 | 2 |
| #64135 | 2 |
| C2×C3×#208 | 2 |
| #63563 | 2 |
| #5215 | 3 |
| #5131 | 3 |