Finite Group DatabasebetaFinite Group DatabasebetaOrder 36224.
504 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 504 conjugacy classes of subgroups — too many to draw. Only its 133 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×#22583630 | C2 | semidirect |
| 2. #31827136 | C2 | semidirect |
| 3. #31826841 | C2 | semidirect |
| 4. #31826699 | C2 | semidirect |
| 5. #31826665 | C2 | semidirect |
| 6. #31826662 | C2 | semidirect |
| 7. #31826610 | C2 | semidirect |
| 8. #31826608 | C2 | semidirect |
| 9. C4×#17985382 | C2 | semidirect |
| 10. D4×C283⋊C8 | C2 | semidirect |
| 11. #550×C283 | C2 | semidirect |
| 51. #17985382 | D4 | semidirect |
| 131. C4×C283 | #135 | semidirect |
| 142. C283 | #3287 | semidirect |
| 146. #550 | D283 | semidirect |
| 276. C4 | #22583630 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22583630 | 2 |
| #31827136 | 2 |
| #31826841 | 2 |
| #31826699 | 2 |
| #31826665 | 2 |
| #31826662 | 2 |
| #31826610 | 2 |
| #31826608 | 2 |
| C4×#17985382 | 2 |
| D4×C283⋊C8 | 2 |
| #550×C283 | 2 |
| #3287 | 283 |