Finite Group DatabasebetaFinite Group DatabasebetaOrder 36224.
456 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 129 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. #31827010 | C2 | semidirect |
| 2. #31826869 | C2 | semidirect |
| 3. #31826840 | C2 | semidirect |
| 4. #31826810 | C2 | semidirect |
| 5. #31826701 | C2 | semidirect |
| 6. #31826699 | C2 | semidirect |
| 7. D8×Dic283 | C2 | semidirect |
| 8. #31826547 | C2 | semidirect |
| 9. #31826545 | C2 | semidirect |
| 10. C2×C8×Dic283 | C2 | semidirect |
| 11. #466×C283 | C2 | semidirect |
| 82. C2×Dic283 | D8 | semidirect |
| 89. C283⋊C8 | #41 | semidirect |
| 101. C8×C283 | #41 | semidirect |
| 127. C283 | #3169 | semidirect |
| 135. #466 | D283 | semidirect |
| 229. C8 | #17985391 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31827010 | 2 |
| #31826869 | 2 |
| #31826840 | 2 |
| #31826810 | 2 |
| #31826701 | 2 |
| #31826699 | 2 |
| D8×Dic283 | 2 |
| #31826547 | 2 |
| #31826545 | 2 |
| C2×C8×Dic283 | 2 |
| #466×C283 | 2 |
| #3169 | 283 |