Finite Group DatabasebetaFinite Group DatabasebetaOrder 36224.
564 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 564 conjugacy classes of subgroups — too many to draw. Only its 137 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. C2×#22583631 | C2 | semidirect |
| 3. #31827016 | C2 | semidirect |
| 4. #31827014 | C2 | semidirect |
| 5. #31826858 | C2 | semidirect |
| 6. #31826857 | C2 | semidirect |
| 7. #31826855 | C2 | semidirect |
| 8. #31826854 | C2 | semidirect |
| 9. #31826851 | C2 | semidirect |
| 10. #97×D283 | C2 | semidirect |
| 11. #497×C283 | C2 | semidirect |
| 65. C8×D283 | D4 | semidirect |
| 133. C283 | #3150 | semidirect |
| 141. #497 | D283 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22583633 | 2 |
| C2×#22583631 | 2 |
| #31827016 | 2 |
| #31827014 | 2 |
| #31826858 | 2 |
| #31826857 | 2 |
| #31826855 | 2 |
| #31826854 | 2 |
| #31826851 | 2 |
| #97×D283 | 2 |
| #497×C283 | 2 |
| #3150 | 283 |