Finite Group DatabasebetaFinite Group DatabasebetaOrder 36224.
408 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 408 conjugacy classes of subgroups — too many to draw. Only its 115 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. #31826994 | C2 | semidirect |
| 3. #31826871 | C2 | semidirect |
| 4. #31826855 | C2 | semidirect |
| 5. #31826830 | C2 | semidirect |
| 6. #31826717 | C2 | semidirect |
| 7. #31826714 | C2 | semidirect |
| 8. #31826550 | C2 | semidirect |
| 9. #31826545 | C2 | semidirect |
| 10. #31826417 | C2 | semidirect |
| 11. #489×C283 | C2 | semidirect |
| 100. C283⋊C8 | #41 | semidirect |
| 137. C283 | #3171 | semidirect |
| 144. #489 | D283 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31827016 | 2 |
| #31826994 | 2 |
| #31826871 | 2 |
| #31826855 | 2 |
| #31826830 | 2 |
| #31826717 | 2 |
| #31826714 | 2 |
| #31826550 | 2 |
| #31826545 | 2 |
| #31826417 | 2 |
| #489×C283 | 2 |
| #3171 | 283 |