Finite Group DatabasebetaFinite Group DatabasebetaOrder 36224.
398 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 398 conjugacy classes of subgroups — too many to draw. Only its 123 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. #31827180 | C2 | semidirect |
| 2. #31827120 | C2 | semidirect |
| 3. #31826816 | C2 | semidirect |
| 4. #31826807 | C2 | semidirect |
| 5. #31826756 | C2 | semidirect |
| 6. #31826694 | C2 | semidirect |
| 7. #31826671 | C2 | semidirect |
| 8. #31826612 | C2 | semidirect |
| 9. C4×D2264 | C2 | semidirect |
| 10. #31826462 | C2 | semidirect |
| 11. C8×D4×C283 | C2 | semidirect |
| 130. C283 | #3303 | semidirect |
| 141. C8×D4 | D283 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31827180 | 2 |
| #31827120 | 2 |
| #31826816 | 2 |
| #31826807 | 2 |
| #31826756 | 2 |
| #31826694 | 2 |
| #31826671 | 2 |
| #31826612 | 2 |
| C4×D2264 | 2 |
| #31826462 | 2 |
| C8×D4×C283 | 2 |
| #3303 | 283 |