Finite Group DatabasebetaFinite Group DatabasebetaOrder 36224.
398 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 398 conjugacy classes of subgroups — too many to draw. Only its 125 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 |
|---|---|---|
| 2. #31826945 | C2 | semidirect |
| 3. #31826805 | C2 | semidirect |
| 4. #31826799 | C2 | semidirect |
| 5. #31826787 | C2 | semidirect |
| 6. #31826777 | C2 | semidirect |
| 7. #31826508 | C2 | semidirect |
| 8. C2×#22583544 | C2 | semidirect |
| 9. #31826466 | C2 | semidirect |
| 10. #31826431 | C2 | semidirect |
| 11. #416×C283 | C2 | semidirect |
| 133. C283 | #3098 | semidirect |
| 144. #416 | D283 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31827043 | 2 |
| #31826945 | 2 |
| #31826805 | 2 |
| #31826799 | 2 |
| #31826787 | 2 |
| #31826777 | 2 |
| #31826508 | 2 |
| C2×#22583544 | 2 |
| #31826466 | 2 |
| #31826431 | 2 |
| #416×C283 | 2 |
| #3098 | 283 |