Finite Group DatabasebetaFinite Group DatabasebetaOrder 36224.
400 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 400 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. #31827020 | C2 | semidirect |
| 3. #31826827 | C2 | semidirect |
| 4. #31826825 | C2 | semidirect |
| 5. #31826824 | C2 | semidirect |
| 6. #31826821 | C2 | semidirect |
| 7. #31826818 | C2 | semidirect |
| 8. #31826472 | C2 | semidirect |
| 10. #31826417 | C2 | semidirect |
| 11. #489×C283 | C2 | semidirect |
| 15. #22583610 | C22 | semidirect |
| 16. #22583601 | C22 | semidirect |
| 30. #22583535 | C22 | semidirect |
| 31. #22583534 | C22 | semidirect |
| 32. #22583533 | C22 | semidirect |
| 36. #22583521 | C22 | semidirect |
| 37. C8×Dic283 | C22 | semidirect |
| 38. C4⋊Q8×C283 | C22 | semidirect |
| 40. #103×C283 | C22 | semidirect |
| 42. #97×C283 | C22 | semidirect |
| 138. C283 | #3140 | semidirect |
| 145. #489 | D283 | semidirect |
| 155. C4⋊Q8 | C2×D283 | semidirect |
| 174. #103 | C2×D283 | semidirect |
| 180. #97 | C2×D283 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31827020 | 2 |
| #124×D283 | 2 |
| #31826827 | 2 |
| #31826825 | 2 |
| #31826824 | 2 |
| #31826821 | 2 |
| #31826818 | 2 |
| #31826472 | 2 |
| #31826468 | 2 |
| #31826417 | 2 |
| #489×C283 | 2 |
| #3140 | 283 |