Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
193 conjugacy classes of subgroups; only the 56 normal subgroups are shown.
This group has 193 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. C3×#904 | C2 | semidirect |
| 2. C2×C3×D24 | C2 | semidirect |
| 3. #63639 | C2 | semidirect |
| 4. #63547 | C2 | semidirect |
| 5. #63545 | C2 | semidirect |
| 11. C3×Dic12 | C22 | semidirect |
| 14. C3×D24 | C22 | semidirect |
| 16. C3⋊(C3⋊C16) | C22 | semidirect |
| 19. #904 | D3 | semidirect |
| 20. C2×D24 | D3 | semidirect |
| 51. Dic12 | C2×D3 | semidirect |
| 54. D24 | C2×D3 | semidirect |
| 124. C32 | #509 | semidirect |
| 153. C3 | #5147 | semidirect |
| 154. C3 | #5193 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#904 | 2 |
| C2×C3×D24 | 2 |
| #63639 | 2 |
| #63547 | 2 |
| #63545 | 2 |
| #5193 | 3 |
| #5147 | 3 |