Finite Group DatabasebetaFinite Group DatabasebetaOrder 36224.
444 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 444 conjugacy classes of subgroups — too many to draw. Only its 121 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. #31826802 | C2 | semidirect |
| 4. #31826742 | C2 | semidirect |
| 5. #31826671 | C2 | semidirect |
| 6. #31826670 | C2 | semidirect |
| 8. #31826564 | C2 | semidirect |
| 9. #31826562 | C2 | semidirect |
| 10. #31826521 | C2 | semidirect |
| 11. #474×C283 | C2 | semidirect |
| 16. #22583610 | C22 | semidirect |
| 21. #22583575 | C22 | semidirect |
| 31. #22583543 | C22 | semidirect |
| 32. C4⋊(C283⋊C8) | C22 | semidirect |
| 33. #22583535 | C22 | semidirect |
| 34. #22583533 | C22 | semidirect |
| 37. #22583520 | C22 | semidirect |
| 38. C4⋊Q8×C283 | C22 | semidirect |
| 40. #107×C283 | C22 | semidirect |
| 41. C4⋊C8×C283 | C22 | semidirect |
| 146. C283 | #3110 | semidirect |
| 152. #474 | D283 | semidirect |
| 164. C4⋊Q8 | C2×D283 | semidirect |
| 181. #107 | C2×D283 | semidirect |
| 183. C4⋊C8 | C2×D283 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31827020 | 2 |
| C4×D4×D283 | 2 |
| #31826802 | 2 |
| #31826742 | 2 |
| #31826671 | 2 |
| #31826670 | 2 |
| #31826617 | 2 |
| #31826564 | 2 |
| #31826562 | 2 |
| #31826521 | 2 |
| #474×C283 | 2 |
| #3110 | 283 |