Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
462 conjugacy classes of subgroups; only the 139 normal subgroups are shown.
This group has 462 conjugacy classes of subgroups — too many to draw. Only its 139 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. C32×#117 | C2 | semidirect |
| 3. C2×#3748 | C2 | semidirect |
| 4. #63632 | C2 | semidirect |
| 10. #3828 | C4 | semidirect |
| 12. C2×C4⋊(C3⋊D3) | C4 | semidirect |
| 14. C2×#634 | C4 | semidirect |
| 17. C32×C42 | C22 | semidirect |
| 19. #3748 | C22 | semidirect |
| 22. C3×#117 | D3 | semidirect |
| 56. C3×C42 | C2×D3 | semidirect |
| 74. #117 | C3⋊D3 | semidirect |
| 114. C42 | C2×C3⋊D3 | semidirect |
| 127. C32 | #421 | semidirect |
| 164. C3 | #5005 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#3828 | 2 |
| C32×#117 | 2 |
| C2×#3748 | 2 |
| #63632 | 2 |
| #5005 | 3 |