Finite Group DatabasebetaFinite Group DatabasebetaOrder 36224.
380 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 121 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 |
|---|---|---|
| 4. #31826747 | C2 | semidirect |
| 5. #31826676 | C2 | semidirect |
| 6. #31826675 | C2 | semidirect |
| 8. #31826571 | C2 | semidirect |
| 9. #31826569 | C2 | semidirect |
| 11. #475×C283 | C2 | semidirect |
| 132. C283 | #3113 | semidirect |
| 138. #475 | D283 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31827020 | 2 |
| C4×Q8×D283 | 2 |
| #31826797 | 2 |
| #31826747 | 2 |
| #31826676 | 2 |
| #31826675 | 2 |
| #31826622 | 2 |
| #31826571 | 2 |
| #31826569 | 2 |
| #31826521 | 2 |
| #475×C283 | 2 |
| #3113 | 283 |