Finite Group DatabasebetaFinite Group DatabasebetaOrder 36224.
354 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 354 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 |
|---|---|---|
| 2. #31827172 | C2 | semidirect |
| 3. #31826870 | C2 | semidirect |
| 4. #31826807 | C2 | semidirect |
| 5. #31826779 | C2 | semidirect |
| 6. #31826761 | C2 | semidirect |
| 7. #31826756 | C2 | semidirect |
| 8. #31826711 | C2 | semidirect |
| 9. C4×#17985381 | C2 | semidirect |
| 10. #31826507 | C2 | semidirect |
| 11. #436×C283 | C2 | semidirect |
| 121. C283 | #3357 | semidirect |
| 132. #436 | D283 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31827180 | 2 |
| #31827172 | 2 |
| #31826870 | 2 |
| #31826807 | 2 |
| #31826779 | 2 |
| #31826761 | 2 |
| #31826756 | 2 |
| #31826711 | 2 |
| C4×#17985381 | 2 |
| #31826507 | 2 |
| #436×C283 | 2 |
| #3357 | 283 |