Finite Group DatabasebetaFinite Group DatabasebetaOrder 36224.
388 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 388 conjugacy classes of subgroups — too many to draw. Only its 131 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. #31827020 | C2 | semidirect |
| 3. #31826771 | C2 | semidirect |
| 4. #31826763 | C2 | semidirect |
| 5. #31826761 | C2 | semidirect |
| 6. #31826755 | C2 | semidirect |
| 7. #31826747 | C2 | semidirect |
| 8. #31826502 | C2 | semidirect |
| 9. C4⋊C8×D283 | C2 | semidirect |
| 11. #474×C283 | C2 | semidirect |
| 44. #17985391 | Q8 | semidirect |
| 134. C283 | #3076 | semidirect |
| 143. #474 | D283 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31827020 | 2 |
| C4×#17985391 | 2 |
| #31826771 | 2 |
| #31826763 | 2 |
| #31826761 | 2 |
| #31826755 | 2 |
| #31826747 | 2 |
| #31826502 | 2 |
| C4⋊C8×D283 | 2 |
| #31826458 | 2 |
| #474×C283 | 2 |
| #3076 | 283 |