Finite Group DatabasebetaFinite Group DatabasebetaOrder 36224.
548 conjugacy classes of subgroups; only the 153 normal subgroups are shown.
This group has 548 conjugacy classes of subgroups — too many to draw. Only its 153 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×#22583636 | C2 | semidirect |
| 2. #31827015 | C2 | semidirect |
| 3. #31826680 | C2 | semidirect |
| 4. #31826670 | C2 | semidirect |
| 5. #31826660 | C2 | semidirect |
| 6. #31826489 | C2 | semidirect |
| 7. #31826464 | C2 | semidirect |
| 8. C2×C4×D4×C283 | C2 | semidirect |
| 14. #22583610 | C22 | semidirect |
| 15. #22583607 | C22 | semidirect |
| 16. #22583598 | C22 | semidirect |
| 21. C4⋊(C283⋊C8) | C22 | semidirect |
| 22. C4⋊(C283⋊C8) | C22 | semidirect |
| 23. #22583533 | C22 | semidirect |
| 24. #22583530 | C22 | semidirect |
| 53. C2×D4×C283 | D4 | semidirect |
| 119. C4×C283 | AGL(1,ℤ/8) | semidirect |
| 129. C283 | #3036 | semidirect |
| 133. C2×C4×D4 | D283 | semidirect |
| 174. C2×D4 | D1132 | semidirect |
| 250. C4 | #22583636 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22583636 | 2 |
| #31827015 | 2 |
| #31826680 | 2 |
| #31826670 | 2 |
| #31826660 | 2 |
| #31826489 | 2 |
| #31826464 | 2 |
| C2×C4×D4×C283 | 2 |
| #3036 | 283 |