Finite Group DatabasebetaFinite Group DatabasebetaOrder 36224.
354 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 354 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. #31827172 | C2 | semidirect |
| 2. #31826868 | C2 | semidirect |
| 3. #31826806 | C2 | semidirect |
| 4. #31826776 | C2 | semidirect |
| 5. #31826757 | C2 | semidirect |
| 6. #31826755 | C2 | semidirect |
| 7. #31826709 | C2 | semidirect |
| 8. C4×#17985380 | C2 | semidirect |
| 9. #31826543 | C2 | semidirect |
| 10. #31826508 | C2 | semidirect |
| 121. C283 | #3357 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31827172 | 2 |
| #31826868 | 2 |
| #31826806 | 2 |
| #31826776 | 2 |
| #31826757 | 2 |
| #31826755 | 2 |
| #31826709 | 2 |
| C4×#17985380 | 2 |
| #31826543 | 2 |
| #31826508 | 2 |
| #555×C283 | 2 |
| #3357 | 283 |