Finite Group DatabasebetaFinite Group DatabasebetaOrder 36224.
396 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 396 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. #31827175 | C2 | semidirect |
| 2. #31827137 | C2 | semidirect |
| 3. #31826830 | C2 | semidirect |
| 4. #31826812 | C2 | semidirect |
| 5. #31826766 | C2 | semidirect |
| 6. #31826756 | C2 | semidirect |
| 7. #31826661 | C2 | semidirect |
| 8. #31826661 | C2 | semidirect |
| 9. #31826578 | C2 | semidirect |
| 10. C4×D2264 | C2 | semidirect |
| 11. #446×C283 | C2 | semidirect |
| 87. D1132 | #41 | semidirect |
| 129. C283 | #3366 | semidirect |
| 139. #446 | D283 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31827175 | 2 |
| #31827137 | 2 |
| #31826830 | 2 |
| #31826812 | 2 |
| #31826766 | 2 |
| #31826756 | 2 |
| #31826661 | 2 |
| #31826578 | 2 |
| C4×D2264 | 2 |
| #446×C283 | 2 |
| #3366 | 283 |