Finite Group DatabasebetaFinite Group DatabasebetaOrder 36224.
342 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 342 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 |
|---|---|---|
| 2. #31826861 | C2 | semidirect |
| 3. #31826803 | C2 | semidirect |
| 4. #31826795 | C2 | semidirect |
| 5. #31826757 | C2 | semidirect |
| 6. #31826750 | C2 | semidirect |
| 7. #31826721 | C2 | semidirect |
| 8. C4×#17985382 | C2 | semidirect |
| 10. #31826505 | C2 | semidirect |
| 116. C283 | #3356 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31827185 | 2 |
| #31826861 | 2 |
| #31826803 | 2 |
| #31826795 | 2 |
| #31826757 | 2 |
| #31826750 | 2 |
| #31826721 | 2 |
| C4×#17985382 | 2 |
| #31826543 | 2 |
| #31826505 | 2 |
| #554×C283 | 2 |
| #3356 | 283 |