Finite Group DatabasebetaFinite Group DatabasebetaOrder 36224.
406 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 406 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. #31827188 | C2 | semidirect |
| 2. #31827137 | C2 | semidirect |
| 3. #31826854 | C2 | semidirect |
| 4. #31826838 | C2 | semidirect |
| 5. #31826681 | C2 | semidirect |
| 6. #31826671 | C2 | semidirect |
| 7. #31826666 | C2 | semidirect |
| 8. #31826661 | C2 | semidirect |
| 9. #31826567 | C2 | semidirect |
| 10. C4×D2264 | C2 | semidirect |
| 11. #446×C283 | C2 | semidirect |
| 106. C8×C283 | #41 | semidirect |
| 132. C283 | #3397 | semidirect |
| 142. #446 | D283 | semidirect |
| 239. C8 | #17985393 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31827188 | 2 |
| #31827137 | 2 |
| #31826854 | 2 |
| #31826838 | 2 |
| #31826681 | 2 |
| #31826671 | 2 |
| #31826666 | 2 |
| #31826661 | 2 |
| #31826567 | 2 |
| C4×D2264 | 2 |
| #446×C283 | 2 |
| #3397 | 283 |