Finite Group DatabasebetaFinite Group DatabasebetaOrder 36224.
372 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 372 conjugacy classes of subgroups — too many to draw. Only its 123 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. Q8×D1132 | C2 | semidirect |
| 3. #31826825 | C2 | semidirect |
| 4. #31826816 | C2 | semidirect |
| 5. #31826761 | C2 | semidirect |
| 6. #31826746 | C2 | semidirect |
| 8. #31826671 | C2 | semidirect |
| 9. #31826567 | C2 | semidirect |
| 11. #446×C283 | C2 | semidirect |
| 122. C283 | #3367 | semidirect |
| 132. #446 | D283 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31827188 | 2 |
| Q8×D1132 | 2 |
| #31826825 | 2 |
| #31826816 | 2 |
| #31826761 | 2 |
| #31826746 | 2 |
| #31826681 | 2 |
| #31826671 | 2 |
| #31826567 | 2 |
| C4×D2264 | 2 |
| #446×C283 | 2 |
| #3367 | 283 |