Finite Group DatabasebetaFinite Group DatabasebetaOrder 36224.
354 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 354 conjugacy classes of subgroups — too many to draw. Only its 115 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. #31827175 | C2 | semidirect |
| 3. #31826868 | C2 | semidirect |
| 4. #31826804 | C2 | semidirect |
| 5. #31826780 | C2 | semidirect |
| 6. #31826756 | C2 | semidirect |
| 7. #31826714 | C2 | semidirect |
| 8. C4×#17985379 | C2 | semidirect |
| 9. #31826542 | C2 | semidirect |
| 10. #31826506 | C2 | semidirect |
| 11. #477×C283 | C2 | semidirect |
| 121. C283 | #3357 | semidirect |
| 128. #477 | D283 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31827181 | 2 |
| #31827175 | 2 |
| #31826868 | 2 |
| #31826804 | 2 |
| #31826780 | 2 |
| #31826756 | 2 |
| #31826714 | 2 |
| C4×#17985379 | 2 |
| #31826542 | 2 |
| #31826506 | 2 |
| #477×C283 | 2 |
| #3357 | 283 |