Finite Group DatabasebetaFinite Group DatabasebetaOrder 36224.
520 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 520 conjugacy classes of subgroups — too many to draw. Only its 157 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. C2×#22583632 | C2 | semidirect |
| 2. #31826976 | C2 | semidirect |
| 3. #31826706 | C2 | semidirect |
| 4. #31826701 | C2 | semidirect |
| 5. #31826694 | C2 | semidirect |
| 6. #31826503 | C2 | semidirect |
| 7. #31826462 | C2 | semidirect |
| 8. C23×C8×C283 | C2 | semidirect |
| 11. C2×Dic1132 | C22 | semidirect |
| 12. C2×#17985381 | C22 | semidirect |
| 13. C2×D2264 | C22 | semidirect |
| 20. #22583544 | C22 | semidirect |
| 21. #22583542 | C22 | semidirect |
| 22. #22583535 | C22 | semidirect |
| 23. #22583532 | C22 | semidirect |
| 56. C2×C8×C283 | D4 | semidirect |
| 91. C22×C283 | #135 | semidirect |
| 106. C283 | #3050 | semidirect |
| 109. C23×C8 | D283 | semidirect |
| 157. C2×C8 | C22⋊D283 | semidirect |
| 200. C22 | #22583632 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22583632 | 2 |
| #31826976 | 2 |
| #31826706 | 2 |
| #31826701 | 2 |
| #31826694 | 2 |
| #31826503 | 2 |
| #31826462 | 2 |
| C23×C8×C283 | 2 |
| #3050 | 283 |