Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
218 conjugacy classes of subgroups; only the 56 normal subgroups are shown.
This group has 218 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. C2×#3745 | C2 | semidirect |
| 2. C3×#904 | C2 | semidirect |
| 3. C3×#812 | C2 | semidirect |
| 4. #63549 | C2 | semidirect |
| 5. #63546 | C2 | semidirect |
| 13. C3×Dic12 | C22 | semidirect |
| 14. C3×D24 | C22 | semidirect |
| 16. C3×C3⋊C16 | C22 | semidirect |
| 18. #904 | D3 | semidirect |
| 25. #812 | D3 | semidirect |
| 50. Dic12 | C2×D3 | semidirect |
| 57. D24 | C2×D3 | semidirect |
| 60. C3⋊C16 | C2×D3 | semidirect |
| 131. C32 | #509 | semidirect |
| 161. C3 | #4908 | semidirect |
| 162. C3 | #5193 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#3745 | 2 |
| C3×#904 | 2 |
| C3×#812 | 2 |
| #63549 | 2 |
| #63546 | 2 |
| #5193 | 3 |
| #4908 | 3 |