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×#22583633 | C2 | semidirect |
| 2. #31827016 | C2 | semidirect |
| 3. C4×#17985393 | C2 | semidirect |
| 4. #31826689 | C2 | semidirect |
| 5. #31826683 | C2 | semidirect |
| 6. #31826667 | C2 | semidirect |
| 7. #31826665 | C2 | semidirect |
| 8. #31826661 | C2 | semidirect |
| 9. C4⋊C8×D283 | C2 | semidirect |
| 10. #31826460 | C2 | semidirect |
| 11. #462×C283 | C2 | semidirect |
| 47. #17985393 | D4 | semidirect |
| 137. C4×C283 | #135 | semidirect |
| 150. C283 | #3035 | semidirect |
| 157. #462 | D283 | semidirect |
| 292. C4 | #22583633 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22583633 | 2 |
| #31827016 | 2 |
| C4×#17985393 | 2 |
| #31826689 | 2 |
| #31826683 | 2 |
| #31826667 | 2 |
| #31826665 | 2 |
| #31826661 | 2 |
| C4⋊C8×D283 | 2 |
| #31826460 | 2 |
| #462×C283 | 2 |
| #3035 | 283 |