Finite Group DatabasebetaFinite Group DatabasebetaOrder 36224.
396 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 396 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. #31827185 | C2 | semidirect |
| 2. #31826811 | C2 | semidirect |
| 3. #31826786 | C2 | semidirect |
| 4. #31826750 | C2 | semidirect |
| 5. #31826692 | C2 | semidirect |
| 6. #31826662 | C2 | semidirect |
| 7. #31826627 | C2 | semidirect |
| 8. C4×#17985382 | C2 | semidirect |
| 9. D4×C283⋊C8 | C2 | semidirect |
| 10. #31826461 | C2 | semidirect |
| 127. C283 | #3304 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31827185 | 2 |
| #31826811 | 2 |
| #31826786 | 2 |
| #31826750 | 2 |
| #31826692 | 2 |
| #31826662 | 2 |
| #31826627 | 2 |
| C4×#17985382 | 2 |
| D4×C283⋊C8 | 2 |
| #31826461 | 2 |
| #550×C283 | 2 |
| #3304 | 283 |