Finite Group DatabasebetaFinite Group DatabasebetaOrder 36224.
430 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 430 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 |
|---|---|---|
| 1. #31827015 | C2 | semidirect |
| 2. C4×#17985392 | C2 | semidirect |
| 3. #31826790 | C2 | semidirect |
| 4. #31826751 | C2 | semidirect |
| 5. #31826746 | C2 | semidirect |
| 6. #31826666 | C2 | semidirect |
| 7. #31826661 | C2 | semidirect |
| 8. #31826612 | C2 | semidirect |
| 9. #31826578 | C2 | semidirect |
| 10. #31826567 | C2 | semidirect |
| 11. #432×C283 | C2 | semidirect |
| 87. Dic566 | #41 | semidirect |
| 93. D1132 | #41 | semidirect |
| 144. C283 | #3115 | semidirect |
| 156. #432 | D283 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31827015 | 2 |
| C4×#17985392 | 2 |
| #31826790 | 2 |
| #31826751 | 2 |
| #31826746 | 2 |
| #31826666 | 2 |
| #31826661 | 2 |
| #31826612 | 2 |
| #31826578 | 2 |
| #31826567 | 2 |
| #432×C283 | 2 |
| #3115 | 283 |