Finite Group DatabasebetaFinite Group DatabasebetaOrder 36224.
492 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 492 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. #31827010 | C2 | semidirect |
| 2. C2×#22583572 | C2 | semidirect |
| 3. #31826778 | C2 | semidirect |
| 4. #31826744 | C2 | semidirect |
| 5. #31826659 | C2 | semidirect |
| 6. #31826601 | C2 | semidirect |
| 7. #31826598 | C2 | semidirect |
| 8. #31826547 | C2 | semidirect |
| 9. #31826545 | C2 | semidirect |
| 10. #31826515 | C2 | semidirect |
| 11. #480×C283 | C2 | semidirect |
| 17. #22583609 | C22 | semidirect |
| 18. #22583606 | C22 | semidirect |
| 22. D4×Dic283 | C22 | semidirect |
| 27. #22583572 | C22 | semidirect |
| 31. #22583543 | C22 | semidirect |
| 32. Dic283⋊C8 | C22 | semidirect |
| 35. #22583530 | C22 | semidirect |
| 37. C8×Dic283 | C22 | semidirect |
| 40. #107×C283 | C22 | semidirect |
| 41. #102×C283 | C22 | semidirect |
| 92. D1132 | #41 | semidirect |
| 99. C2×Dic283 | D8 | semidirect |
| 149. C283 | #3100 | semidirect |
| 154. #480 | D283 | semidirect |
| 184. #107 | C2×D283 | semidirect |
| 189. #102 | C2×D283 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31827010 | 2 |
| C2×#22583572 | 2 |
| #31826778 | 2 |
| #31826744 | 2 |
| #31826659 | 2 |
| #31826601 | 2 |
| #31826598 | 2 |
| #31826547 | 2 |
| #31826545 | 2 |
| #31826515 | 2 |
| #480×C283 | 2 |
| #3100 | 283 |