Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
786 conjugacy classes of subgroups; only the 219 normal subgroups are shown.
This group has 786 conjugacy classes of subgroups — too many to draw. Only its 219 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×#3828 | C2 | semidirect |
| 2. C2×C32×M16 | C2 | semidirect |
| 3. #64118 | C2 | semidirect |
| 4. #64117 | C2 | semidirect |
| 5. #64113 | C2 | semidirect |
| 12. #3828 | C22 | semidirect |
| 13. C2×C4⋊(C3⋊D3) | C22 | semidirect |
| 15. C2×#634 | C22 | semidirect |
| 16. C32×M16 | C22 | semidirect |
| 17. C2×C32×C8 | C22 | semidirect |
| 18. #3746 | C22 | semidirect |
| 19. #3745 | C22 | semidirect |
| 20. #3744 | C22 | semidirect |
| 22. C2×C3×M16 | D3 | semidirect |
| 52. C3×M16 | C2×D3 | semidirect |
| 53. C2×C3×C8 | C2×D3 | semidirect |
| 70. C2×M16 | C3⋊D3 | semidirect |
| 103. M16 | C2×C3⋊D3 | semidirect |
| 104. C2×C8 | C2×C3⋊D3 | semidirect |
| 114. C32 | #575 | semidirect |
| 144. C3 | #5748 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#3828 | 2 |
| C2×C32×M16 | 2 |
| #64118 | 2 |
| #64117 | 2 |
| #64113 | 2 |
| #5748 | 3 |