Finite Group DatabasebetaFinite Group DatabasebetaOrder 36224.
548 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 548 conjugacy classes of subgroups — too many to draw. Only its 145 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×#22583638 | C2 | semidirect |
| 2. #31827015 | C2 | semidirect |
| 3. C2×C4×D1132 | C2 | semidirect |
| 4. #31826681 | C2 | semidirect |
| 5. #31826671 | C2 | semidirect |
| 6. #31826661 | C2 | semidirect |
| 7. #31826467 | C2 | semidirect |
| 8. #423×C283 | C2 | semidirect |
| 15. #22583610 | C22 | semidirect |
| 16. #22583607 | C22 | semidirect |
| 17. #22583598 | C22 | semidirect |
| 28. #22583535 | C22 | semidirect |
| 29. #22583532 | C22 | semidirect |
| 32. C4⋊C8×C283 | C22 | semidirect |
| 33. C4⋊C8×C283 | C22 | semidirect |
| 42. C2×D1132 | D4 | semidirect |
| 118. C4×C283 | AGL(1,ℤ/8) | semidirect |
| 129. C283 | #3036 | semidirect |
| 137. #423 | D283 | semidirect |
| 160. C4⋊C8 | C2×D283 | semidirect |
| 161. C4⋊C8 | C2×D283 | semidirect |
| 250. C4 | #22583638 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22583638 | 2 |
| #31827015 | 2 |
| C2×C4×D1132 | 2 |
| #31826681 | 2 |
| #31826671 | 2 |
| #31826661 | 2 |
| #31826467 | 2 |
| #423×C283 | 2 |
| #3036 | 283 |