Finite Group DatabasebetaFinite Group DatabasebetaOrder 36224.
430 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 430 conjugacy classes of subgroups — too many to draw. Only its 119 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. #31827016 | C2 | semidirect |
| 2. C4×#17985391 | C2 | semidirect |
| 3. #31826792 | C2 | semidirect |
| 4. #31826747 | C2 | semidirect |
| 5. #31826666 | C2 | semidirect |
| 6. #31826660 | C2 | semidirect |
| 7. #31826611 | C2 | semidirect |
| 8. #31826574 | C2 | semidirect |
| 9. #31826564 | C2 | semidirect |
| 10. #31826521 | C2 | semidirect |
| 11. #474×C283 | C2 | semidirect |
| 86. Dic566 | #41 | semidirect |
| 109. D4×C283 | #41 | semidirect |
| 144. C283 | #3115 | semidirect |
| 150. #474 | D283 | semidirect |
| 241. D4 | #17985393 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31827016 | 2 |
| C4×#17985391 | 2 |
| #31826792 | 2 |
| #31826747 | 2 |
| #31826666 | 2 |
| #31826660 | 2 |
| #31826611 | 2 |
| #31826574 | 2 |
| #31826564 | 2 |
| #31826521 | 2 |
| #474×C283 | 2 |
| #3115 | 283 |