Finite Group DatabasebetaFinite Group DatabasebetaOrder 36224.
450 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 450 conjugacy classes of subgroups — too many to draw. Only its 117 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. #31827001 | C2 | semidirect |
| 2. C2×#22583572 | C2 | semidirect |
| 3. #31826778 | C2 | semidirect |
| 4. #31826764 | C2 | semidirect |
| 5. #31826683 | C2 | semidirect |
| 6. #31826615 | C2 | semidirect |
| 8. #31826576 | C2 | semidirect |
| 9. #31826568 | C2 | semidirect |
| 10. #31826519 | C2 | semidirect |
| 11. #483×C283 | C2 | semidirect |
| 17. #22583601 | C22 | semidirect |
| 18. #22583599 | C22 | semidirect |
| 21. Q8×Dic283 | C22 | semidirect |
| 26. #22583572 | C22 | semidirect |
| 31. #22583543 | C22 | semidirect |
| 32. Dic283⋊C8 | C22 | semidirect |
| 35. #22583530 | C22 | semidirect |
| 37. #22583520 | C22 | semidirect |
| 40. #106×C283 | C22 | semidirect |
| 41. #103×C283 | C22 | semidirect |
| 140. C283 | #3114 | semidirect |
| 144. #483 | D283 | semidirect |
| 175. #106 | C2×D283 | semidirect |
| 177. #103 | C2×D283 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31827001 | 2 |
| C2×#22583572 | 2 |
| #31826778 | 2 |
| #31826764 | 2 |
| #31826683 | 2 |
| #31826615 | 2 |
| #31826601 | 2 |
| #31826576 | 2 |
| #31826568 | 2 |
| #31826519 | 2 |
| #483×C283 | 2 |
| #3114 | 283 |