Finite Group DatabasebetaFinite Group DatabasebetaOrder 36224.
336 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 336 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. #31827193 | C2 | semidirect |
| 3. #31826815 | C2 | semidirect |
| 4. #31826772 | C2 | semidirect |
| 7. #31826672 | C2 | semidirect |
| 8. Q8×C283⋊C8 | C2 | semidirect |
| 9. C4×#17985382 | C2 | semidirect |
| 115. C283 | #3364 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31827193 | 2 |
| #31826819 | 2 |
| #31826815 | 2 |
| #31826772 | 2 |
| #31826745 | 2 |
| #31826684 | 2 |
| #31826672 | 2 |
| Q8×C283⋊C8 | 2 |
| C4×#17985382 | 2 |
| C4×#17985380 | 2 |
| #556×C283 | 2 |
| #3364 | 283 |