Finite Group DatabasebetaFinite Group DatabasebetaOrder 36224.
496 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 496 conjugacy classes of subgroups — too many to draw. Only its 131 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×#22583631 | C2 | semidirect |
| 2. #31827016 | C2 | semidirect |
| 3. C4×#17985391 | C2 | semidirect |
| 4. #31826690 | C2 | semidirect |
| 5. #31826682 | C2 | semidirect |
| 6. #31826672 | C2 | semidirect |
| 7. #31826666 | C2 | semidirect |
| 8. #31826660 | C2 | semidirect |
| 9. C4⋊C8×D283 | C2 | semidirect |
| 10. #31826460 | C2 | semidirect |
| 11. #461×C283 | C2 | semidirect |
| 47. #17985391 | D4 | semidirect |
| 136. C4×C283 | #135 | semidirect |
| 150. C283 | #3035 | semidirect |
| 158. #461 | D283 | semidirect |
| 292. C4 | #22583631 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22583631 | 2 |
| #31827016 | 2 |
| C4×#17985391 | 2 |
| #31826690 | 2 |
| #31826682 | 2 |
| #31826672 | 2 |
| #31826666 | 2 |
| #31826660 | 2 |
| C4⋊C8×D283 | 2 |
| #31826460 | 2 |
| #461×C283 | 2 |
| #3035 | 283 |