Finite Group DatabasebetaFinite Group DatabasebetaOrder 36224.
532 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 532 conjugacy classes of subgroups — too many to draw. Only its 149 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. C2×#22583641 | C2 | semidirect |
| 2. C2×#22583640 | C2 | semidirect |
| 4. C22×#17985382 | C2 | semidirect |
| 5. #31827041 | C2 | semidirect |
| 6. #31826860 | C2 | semidirect |
| 7. #31826857 | C2 | semidirect |
| 8. #31826847 | C2 | semidirect |
| 9. #31826844 | C2 | semidirect |
| 10. #31826421 | C2 | semidirect |
| 11. #536×C283 | C2 | semidirect |
| 143. C283 | #3156 | semidirect |
| 150. #536 | D283 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22583641 | 2 |
| C2×#22583640 | 2 |
| C2×#22583630 | 2 |
| C22×#17985382 | 2 |
| #31827041 | 2 |
| #31826860 | 2 |
| #31826857 | 2 |
| #31826847 | 2 |
| #31826844 | 2 |
| #31826421 | 2 |
| #536×C283 | 2 |
| #3156 | 283 |