Finite Group DatabasebetaFinite Group DatabasebetaOrder 36224.
386 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 386 conjugacy classes of subgroups — too many to draw. Only its 119 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. #31826804 | C2 | semidirect |
| 4. #31826760 | C2 | semidirect |
| 5. #31826756 | C2 | semidirect |
| 6. #31826667 | C2 | semidirect |
| 8. #31826572 | C2 | semidirect |
| 9. #31826568 | C2 | semidirect |
| 10. #31826521 | C2 | semidirect |
| 11. #462×C283 | C2 | semidirect |
| 136. C283 | #3116 | semidirect |
| 143. #462 | D283 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31827020 | 2 |
| C4×#17985393 | 2 |
| #31826804 | 2 |
| #31826760 | 2 |
| #31826756 | 2 |
| #31826667 | 2 |
| #31826626 | 2 |
| #31826572 | 2 |
| #31826568 | 2 |
| #31826521 | 2 |
| #462×C283 | 2 |
| #3116 | 283 |