Finite Group DatabasebetaFinite Group DatabasebetaOrder 36224.
492 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 129 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×D4×Dic283 | C2 | semidirect |
| 3. #31826779 | C2 | semidirect |
| 4. #31826776 | C2 | semidirect |
| 5. #31826743 | C2 | semidirect |
| 6. #31826658 | C2 | semidirect |
| 7. #31826599 | C2 | semidirect |
| 8. D8×Dic283 | C2 | semidirect |
| 9. #31826545 | C2 | semidirect |
| 10. #31826515 | C2 | semidirect |
| 11. #447×C283 | C2 | semidirect |
| 15. #22583609 | C22 | semidirect |
| 16. #22583606 | C22 | semidirect |
| 24. D4×Dic283 | C22 | semidirect |
| 25. #22583572 | C22 | semidirect |
| 30. #22583544 | C22 | semidirect |
| 31. #22583543 | C22 | semidirect |
| 32. Dic283⋊C8 | C22 | semidirect |
| 33. #22583532 | C22 | semidirect |
| 35. #22583531 | C22 | semidirect |
| 37. C8×Dic283 | C22 | semidirect |
| 96. C2×Dic283 | D8 | semidirect |
| 113. D4×C283 | #41 | semidirect |
| 149. C283 | #3100 | semidirect |
| 158. #447 | D283 | semidirect |
| 249. D4 | #17985391 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31827010 | 2 |
| C2×D4×Dic283 | 2 |
| #31826779 | 2 |
| #31826776 | 2 |
| #31826743 | 2 |
| #31826658 | 2 |
| #31826599 | 2 |
| D8×Dic283 | 2 |
| #31826545 | 2 |
| #31826515 | 2 |
| #447×C283 | 2 |
| #3100 | 283 |