Finite Group DatabasebetaFinite Group DatabasebetaOrder 36224.
342 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 342 conjugacy classes of subgroups — too many to draw. Only its 117 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 |
|---|---|---|
| 3. #31826863 | C2 | semidirect |
| 4. #31826804 | C2 | semidirect |
| 5. #31826794 | C2 | semidirect |
| 6. #31826760 | C2 | semidirect |
| 7. #31826750 | C2 | semidirect |
| 8. #31826720 | C2 | semidirect |
| 10. #31826506 | C2 | semidirect |
| 11. C4×Q16×C283 | C2 | semidirect |
| 116. C283 | #3356 | semidirect |
| 126. C4×Q16 | D283 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31827188 | 2 |
| #31827175 | 2 |
| #31826863 | 2 |
| #31826804 | 2 |
| #31826794 | 2 |
| #31826760 | 2 |
| #31826750 | 2 |
| #31826720 | 2 |
| #31826544 | 2 |
| #31826506 | 2 |
| C4×Q16×C283 | 2 |
| #3356 | 283 |