Finite Group DatabasebetaFinite Group DatabasebetaOrder 36224.
284 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 284 conjugacy classes of subgroups — too many to draw. Only its 71 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. #31826515 | C2 | semidirect |
| 3. #31826316 | C2 | semidirect |
| 4. #31826200 | C2 | semidirect |
| 5. #31826199 | C2 | semidirect |
| 6. #31826198 | C2 | semidirect |
| 7. #327×C283 | C2 | semidirect |
| 9. #22583609 | C4 | semidirect |
| 10. #22583606 | C4 | semidirect |
| 14. D4×Dic283 | C4 | semidirect |
| 15. #22583572 | C4 | semidirect |
| 120. C283 | #1502 | semidirect |
| 128. #327 | D283 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31827010 | 2 |
| #31826515 | 2 |
| #31826316 | 2 |
| #31826200 | 2 |
| #31826199 | 2 |
| #31826198 | 2 |
| #327×C283 | 2 |
| #1502 | 283 |