Finite Group DatabasebetaFinite Group DatabasebetaOrder 36224.
492 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 181 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 |
|---|---|---|
| 2. #31826942 | C2 | semidirect |
| 4. #31826562 | C2 | semidirect |
| 5. #31826556 | C2 | semidirect |
| 6. #31826501 | C2 | semidirect |
| 7. #31826475 | C2 | semidirect |
| 8. #31826423 | C2 | semidirect |
| 11. C2×#17985380 | C4 | semidirect |
| 16. #22583575 | C22 | semidirect |
| 23. #22583543 | C22 | semidirect |
| 24. #22583541 | C22 | semidirect |
| 25. #22583535 | C22 | semidirect |
| 26. #22583520 | C22 | semidirect |
| 27. C8×Dic283 | C22 | semidirect |
| 34. C2×Dic566 | C2×C4 | semidirect |
| 38. #17985380 | C2×C4 | semidirect |
| 39. #17985380 | C2×C4 | semidirect |
| 40. C2×C283⋊C8 | C2×C4 | semidirect |
| 103. C283 | #2949 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#17985380 | 2 |
| #31826942 | 2 |
| #31826940 | 2 |
| #31826562 | 2 |
| #31826556 | 2 |
| #31826501 | 2 |
| #31826475 | 2 |
| #31826423 | 2 |
| #418×C283 | 2 |
| #2949 | 283 |