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. #31827013 | C2 | semidirect |
| 3. C4×#17985393 | C2 | semidirect |
| 4. #31826685 | C2 | semidirect |
| 5. #31826679 | C2 | semidirect |
| 6. #31826675 | C2 | semidirect |
| 7. #31826671 | C2 | semidirect |
| 8. #31826657 | C2 | semidirect |
| 9. C4⋊C8×D283 | C2 | semidirect |
| 10. #31826458 | C2 | semidirect |
| 11. #460×C283 | C2 | semidirect |
| 45. #17985393 | D4 | semidirect |
| 136. C4×C283 | #135 | semidirect |
| 150. C283 | #3035 | semidirect |
| 159. #460 | 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 |
| #31827013 | 2 |
| C4×#17985393 | 2 |
| #31826685 | 2 |
| #31826679 | 2 |
| #31826675 | 2 |
| #31826671 | 2 |
| #31826657 | 2 |
| C4⋊C8×D283 | 2 |
| #31826458 | 2 |
| #460×C283 | 2 |
| #3035 | 283 |