Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
774 conjugacy classes of subgroups; only the 219 normal subgroups are shown.
This group has 774 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. #64367 | C2 | semidirect |
| 2. #64366 | C2 | semidirect |
| 3. C32×#131 | C2 | semidirect |
| 4. #64118 | C2 | semidirect |
| 5. #64117 | C2 | semidirect |
| 6. #64113 | C2 | semidirect |
| 7. C2×#3744 | C2 | semidirect |
| 15. #3828 | C22 | semidirect |
| 17. C2×#634 | C22 | semidirect |
| 18. C32×M16 | C22 | semidirect |
| 19. C2×C32×C8 | C22 | semidirect |
| 20. #3746 | C22 | semidirect |
| 21. #3745 | C22 | semidirect |
| 22. #3744 | C22 | semidirect |
| 23. #3744 | C22 | semidirect |
| 24. #3744 | C22 | semidirect |
| 27. C3×#131 | D3 | semidirect |
| 59. C3×M16 | C2×D3 | semidirect |
| 60. C2×C3×C8 | C2×D3 | semidirect |
| 80. #131 | C3⋊D3 | semidirect |
| 116. M16 | C2×C3⋊D3 | semidirect |
| 117. C2×C8 | C2×C3⋊D3 | semidirect |
| 126. C32 | #577 | semidirect |
| 156. C3 | #5751 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #64367 | 2 |
| #64366 | 2 |
| C32×#131 | 2 |
| #64118 | 2 |
| #64117 | 2 |
| #64113 | 2 |
| C2×#3744 | 2 |
| #5751 | 3 |