Finite Group DatabasebetaFinite Group DatabasebetaOrder 36224.
484 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 484 conjugacy classes of subgroups — too many to draw. Only its 131 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. C2×#22583642 | C2 | semidirect |
| 3. C4×Q8×D283 | C2 | semidirect |
| 4. #31826690 | C2 | semidirect |
| 5. #31826689 | C2 | semidirect |
| 6. #31826672 | C2 | semidirect |
| 7. #31826666 | C2 | semidirect |
| 8. #31826665 | C2 | semidirect |
| 9. #31826487 | C2 | semidirect |
| 10. #31826465 | C2 | semidirect |
| 11. #462×C283 | C2 | semidirect |
| 49. Q8×D283 | D4 | semidirect |
| 133. C4×C283 | #137 | semidirect |
| 146. C283 | #3037 | semidirect |
| 154. #462 | D283 | semidirect |
| 285. C4 | #22583642 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22583642 | 2 |
| #31827016 | 2 |
| C4×Q8×D283 | 2 |
| #31826690 | 2 |
| #31826689 | 2 |
| #31826672 | 2 |
| #31826666 | 2 |
| #31826665 | 2 |
| #31826487 | 2 |
| #31826465 | 2 |
| #462×C283 | 2 |
| #3037 | 283 |