Finite Group DatabasebetaFinite Group DatabasebetaOrder 36224.
348 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 348 conjugacy classes of subgroups — too many to draw. Only its 125 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 |
|---|---|---|
| 2. #31826822 | C2 | semidirect |
| 4. #31826762 | C2 | semidirect |
| 5. #31826747 | C2 | semidirect |
| 6. #31826687 | C2 | semidirect |
| 8. Q8×C283⋊C8 | C2 | semidirect |
| 9. C4×#17985382 | C2 | semidirect |
| 10. C4×#17985379 | C2 | semidirect |
| 11. #557×C283 | C2 | semidirect |
| 117. C283 | #3365 | semidirect |
| 120. #557 | D283 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31827200 | 2 |
| #31826822 | 2 |
| #31826813 | 2 |
| #31826762 | 2 |
| #31826747 | 2 |
| #31826687 | 2 |
| #31826665 | 2 |
| Q8×C283⋊C8 | 2 |
| C4×#17985382 | 2 |
| C4×#17985379 | 2 |
| #557×C283 | 2 |
| #3365 | 283 |