Finite Group DatabasebetaFinite Group DatabasebetaOrder 36224.
418 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 418 conjugacy classes of subgroups — too many to draw. Only its 125 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. #31827200 | C2 | semidirect |
| 2. #31827137 | C2 | semidirect |
| 3. #31826854 | C2 | semidirect |
| 4. #31826842 | C2 | semidirect |
| 5. #31826681 | C2 | semidirect |
| 6. #31826666 | C2 | semidirect |
| 7. #31826661 | C2 | semidirect |
| 8. #31826661 | C2 | semidirect |
| 9. #31826578 | C2 | semidirect |
| 10. C4×#17985381 | C2 | semidirect |
| 11. #446×C283 | C2 | semidirect |
| 108. C8×C283 | #41 | semidirect |
| 134. C283 | #3399 | semidirect |
| 144. #446 | D283 | semidirect |
| 243. C8 | #17985393 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31827200 | 2 |
| #31827137 | 2 |
| #31826854 | 2 |
| #31826842 | 2 |
| #31826681 | 2 |
| #31826666 | 2 |
| #31826661 | 2 |
| #31826578 | 2 |
| C4×#17985381 | 2 |
| #446×C283 | 2 |
| #3399 | 283 |