Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
211 conjugacy classes of subgroups; only the 56 normal subgroups are shown.
This group has 211 conjugacy classes of subgroups — too many to draw. Only its 56 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. #64113 | C2 | semidirect |
| 2. C2×C3×D24 | C2 | semidirect |
| 3. C3×#812 | C2 | semidirect |
| 4. #63548 | C2 | semidirect |
| 5. #63546 | C2 | semidirect |
| 11. #3746 | C22 | semidirect |
| 12. #3745 | C22 | semidirect |
| 16. C3×C3⋊C16 | C22 | semidirect |
| 21. C2×D24 | D3 | semidirect |
| 25. #812 | D3 | semidirect |
| 61. C3⋊C16 | C2×D3 | semidirect |
| 133. C32 | #509 | semidirect |
| 163. C3 | #4908 | semidirect |
| 164. C3 | #5147 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #64113 | 2 |
| C2×C3×D24 | 2 |
| C3×#812 | 2 |
| #63548 | 2 |
| #63546 | 2 |
| #5147 | 3 |
| #4908 | 3 |