Finite Group DatabasebetaFinite Group DatabasebetaOrder 36224.
526 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 526 conjugacy classes of subgroups — too many to draw. Only its 141 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. C22×#17985377 | C2 | semidirect |
| 2. #31827029 | C2 | semidirect |
| 3. #31826940 | C2 | semidirect |
| 4. #31826682 | C2 | semidirect |
| 5. #31826658 | C2 | semidirect |
| 6. #31826493 | C2 | semidirect |
| 7. #31826471 | C2 | semidirect |
| 8. #31826461 | C2 | semidirect |
| 9. C2×AGL(1,ℤ/8)×C283 | C2 | semidirect |
| 14. #22583606 | C22 | semidirect |
| 15. #22583599 | C22 | semidirect |
| 19. D4×Dic283 | C22 | semidirect |
| 23. Dic283⋊C8 | C22 | semidirect |
| 24. #22583534 | C22 | semidirect |
| 25. #22583532 | C22 | semidirect |
| 26. #22583531 | C22 | semidirect |
| 30. C2×SD16×C283 | C22 | semidirect |
| 31. C2×D8×C283 | C22 | semidirect |
| 58. C2×D4×C283 | D4 | semidirect |
| 121. C283 | #3041 | semidirect |
| 123. C2×AGL(1,ℤ/8) | D283 | semidirect |
| 136. C2×SD16 | C2×D283 | semidirect |
| 139. C2×D8 | C2×D283 | semidirect |
| 168. C2×D4 | C22⋊D283 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#17985377 | 2 |
| #31827029 | 2 |
| #31826940 | 2 |
| #31826682 | 2 |
| #31826658 | 2 |
| #31826493 | 2 |
| #31826471 | 2 |
| #31826461 | 2 |
| C2×AGL(1,ℤ/8)×C283 | 2 |
| #3041 | 283 |