Finite Group DatabasebetaFinite Group DatabasebetaOrder 36224.
430 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 430 conjugacy classes of subgroups — too many to draw. Only its 119 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. #31827016 | C2 | semidirect |
| 2. C4×#17985393 | C2 | semidirect |
| 3. #31826791 | C2 | semidirect |
| 4. #31826742 | C2 | semidirect |
| 5. #31826665 | C2 | semidirect |
| 6. #31826661 | C2 | semidirect |
| 7. #31826613 | C2 | semidirect |
| 8. #31826576 | C2 | semidirect |
| 9. #31826568 | C2 | semidirect |
| 10. #31826521 | C2 | semidirect |
| 11. #475×C283 | C2 | semidirect |
| 93. D1132 | #41 | semidirect |
| 109. Q8×C283 | #41 | semidirect |
| 144. C283 | #3115 | semidirect |
| 149. #475 | D283 | semidirect |
| 233. Q8 | #17985393 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31827016 | 2 |
| C4×#17985393 | 2 |
| #31826791 | 2 |
| #31826742 | 2 |
| #31826665 | 2 |
| #31826661 | 2 |
| #31826613 | 2 |
| #31826576 | 2 |
| #31826568 | 2 |
| #31826521 | 2 |
| #475×C283 | 2 |
| #3115 | 283 |