Finite Group DatabasebetaFinite Group DatabasebetaOrder 36224.
492 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 149 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×#17985381 | C2 | semidirect |
| 2. #31827036 | C2 | semidirect |
| 4. #31826711 | C2 | semidirect |
| 5. #31826694 | C2 | semidirect |
| 6. #31826503 | C2 | semidirect |
| 7. #31826475 | C2 | semidirect |
| 8. #31826471 | C2 | semidirect |
| 9. C2×#131×C283 | C2 | semidirect |
| 20. #22583589 | C22 | semidirect |
| 25. #22583544 | C22 | semidirect |
| 26. #22583542 | C22 | semidirect |
| 27. #22583535 | C22 | semidirect |
| 32. C2×M16×C283 | C22 | semidirect |
| 34. C22×C8×C283 | C22 | semidirect |
| 67. C2×C8×C283 | D4 | semidirect |
| 120. C283 | #3057 | semidirect |
| 123. C2×#131 | D283 | semidirect |
| 139. C2×M16 | C2×D283 | semidirect |
| 141. C22×C8 | C2×D283 | semidirect |
| 179. C2×C8 | C22⋊D283 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#17985381 | 2 |
| #31827036 | 2 |
| #31827029 | 2 |
| #31826711 | 2 |
| #31826694 | 2 |
| #31826503 | 2 |
| #31826475 | 2 |
| #31826471 | 2 |
| C2×#131×C283 | 2 |
| #3057 | 283 |