Finite Group DatabasebetaFinite Group DatabasebetaOrder 36224.
372 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 372 conjugacy classes of subgroups — too many to draw. Only its 117 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. #31827201 | C2 | semidirect |
| 2. #31827189 | C2 | semidirect |
| 3. #31826846 | C2 | semidirect |
| 4. #31826685 | C2 | semidirect |
| 5. #31826682 | C2 | semidirect |
| 6. #31826672 | C2 | semidirect |
| 8. C8×Dic566 | C2 | semidirect |
| 9. C4×#17985381 | C2 | semidirect |
| 10. SD16×Dic283 | C2 | semidirect |
| 11. #492×C283 | C2 | semidirect |
| 125. C283 | #3394 | semidirect |
| 130. #492 | D283 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31827201 | 2 |
| #31827189 | 2 |
| #31826846 | 2 |
| #31826685 | 2 |
| #31826682 | 2 |
| #31826672 | 2 |
| #31826657 | 2 |
| C8×Dic566 | 2 |
| C4×#17985381 | 2 |
| SD16×Dic283 | 2 |
| #492×C283 | 2 |
| #3394 | 283 |