Finite Group DatabasebetaFinite Group DatabasebetaOrder 36224.
384 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 384 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. #31827200 | C2 | semidirect |
| 2. #31826847 | C2 | semidirect |
| 4. #31826680 | C2 | semidirect |
| 5. #31826677 | C2 | semidirect |
| 6. #31826665 | C2 | semidirect |
| 7. #31826662 | C2 | semidirect |
| 8. Q8×C283⋊C8 | C2 | semidirect |
| 9. C4×#17985382 | C2 | semidirect |
| 10. C4×#17985377 | C2 | semidirect |
| 11. #559×C283 | C2 | semidirect |
| 127. C283 | #3396 | semidirect |
| 130. #559 | D283 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31827200 | 2 |
| #31826847 | 2 |
| #31826841 | 2 |
| #31826680 | 2 |
| #31826677 | 2 |
| #31826665 | 2 |
| #31826662 | 2 |
| Q8×C283⋊C8 | 2 |
| C4×#17985382 | 2 |
| C4×#17985377 | 2 |
| #559×C283 | 2 |
| #3396 | 283 |