Finite Group DatabasebetaFinite Group DatabasebetaOrder 36224.
504 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 504 conjugacy classes of subgroups — too many to draw. Only its 123 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×#22583632 | C2 | semidirect |
| 2. C2×#22583629 | C2 | semidirect |
| 3. #31827133 | C2 | semidirect |
| 4. #31826840 | C2 | semidirect |
| 5. #31826702 | C2 | semidirect |
| 6. #31826664 | C2 | semidirect |
| 7. #31826611 | C2 | semidirect |
| 8. #31826608 | C2 | semidirect |
| 9. #31826559 | C2 | semidirect |
| 10. C8×C22⋊D283 | C2 | semidirect |
| 11. #466×C283 | C2 | semidirect |
| 56. Dic1132 | D4 | semidirect |
| 134. Dic283 | #135 | semidirect |
| 142. C283 | #3287 | semidirect |
| 149. #466 | D283 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22583632 | 2 |
| C2×#22583629 | 2 |
| #31827133 | 2 |
| #31826840 | 2 |
| #31826702 | 2 |
| #31826664 | 2 |
| #31826611 | 2 |
| #31826608 | 2 |
| #31826559 | 2 |
| C8×C22⋊D283 | 2 |
| #466×C283 | 2 |
| #3287 | 283 |