Finite Group DatabasebetaFinite Group DatabasebetaOrder 36224.
408 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 408 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. #31827000 | C2 | semidirect |
| 3. #31826854 | C2 | semidirect |
| 4. #31826831 | C2 | semidirect |
| 5. #31826827 | C2 | semidirect |
| 6. #31826719 | C2 | semidirect |
| 7. #31826712 | C2 | semidirect |
| 8. #31826552 | C2 | semidirect |
| 9. #31826547 | C2 | semidirect |
| 10. #31826417 | C2 | semidirect |
| 11. #501×C283 | C2 | semidirect |
| 110. C8×C283 | #41 | semidirect |
| 137. C283 | #3171 | semidirect |
| 141. #501 | D283 | semidirect |
| 248. C8 | #17985393 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31827016 | 2 |
| #31827000 | 2 |
| #31826854 | 2 |
| #31826831 | 2 |
| #31826827 | 2 |
| #31826719 | 2 |
| #31826712 | 2 |
| #31826552 | 2 |
| #31826547 | 2 |
| #31826417 | 2 |
| #501×C283 | 2 |
| #3171 | 283 |