Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
570 conjugacy classes of subgroups; only the 136 normal subgroups are shown.
This group has 570 conjugacy classes of subgroups — too many to draw. Only its 136 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×#3796 | C2 | semidirect |
| 2. C2×C8×C3⋊D3 | C2 | semidirect |
| 3. C2×C3×Dic12 | C2 | semidirect |
| 4. C2×C3×D24 | C2 | semidirect |
| 5. C2×#3715 | C2 | semidirect |
| 6. #63810 | C2 | direct (N × H) |
| 15. #3796 | C22 | semidirect |
| 18. C8×C3⋊D3 | C22 | semidirect |
| 19. C3×Dic12 | C22 | semidirect |
| 20. C3×D24 | C22 | semidirect |
| 21. #3715 | C22 | semidirect |
| 30. C2×Dic12 | D3 | semidirect |
| 31. C2×D24 | D3 | semidirect |
| 76. Dic12 | C2×D3 | semidirect |
| 77. D24 | C2×D3 | semidirect |
| 133. C2×C32 | #135 | semidirect |
| 174. C32 | C2×#135 | semidirect |
| 193. C2×C3 | #912 | semidirect |
| 194. C2×C3 | #919 | semidirect |
| 211. C3 | C2×#912 | semidirect |
| 212. C3 | C2×#919 | semidirect |
| 215. C2 | #63810 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#3796 | 2 |
| C2×C8×C3⋊D3 | 2 |
| C2×C3×Dic12 | 2 |
| C2×C3×D24 | 2 |
| C2×#3715 | 2 |
| #63810 | 2 |
| C2×#919 | 3 |
| C2×#912 | 3 |