Finite Group DatabasebetaFinite Group DatabasebetaOrder 36224.
400 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 400 conjugacy classes of subgroups — too many to draw. Only its 129 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. #31827018 | C2 | semidirect |
| 3. #31826821 | C2 | semidirect |
| 4. #31826818 | C2 | semidirect |
| 5. #31826814 | C2 | semidirect |
| 6. #31826810 | C2 | semidirect |
| 7. #31826462 | C2 | semidirect |
| 8. #31826461 | C2 | semidirect |
| 9. #31826459 | C2 | semidirect |
| 10. C2×C8×Dic283 | C2 | semidirect |
| 11. #416×C283 | C2 | semidirect |
| 125. C283 | #3131 | semidirect |
| 136. #416 | D283 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31827018 | 2 |
| #31827011 | 2 |
| #31826821 | 2 |
| #31826818 | 2 |
| #31826814 | 2 |
| #31826810 | 2 |
| #31826462 | 2 |
| #31826461 | 2 |
| #31826459 | 2 |
| C2×C8×Dic283 | 2 |
| #416×C283 | 2 |
| #3131 | 283 |