Finite Group DatabasebetaFinite Group DatabasebetaOrder 36224.
398 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 398 conjugacy classes of subgroups — too many to draw. Only its 117 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. #31827180 | C2 | semidirect |
| 2. #31827119 | C2 | semidirect |
| 3. #31826816 | C2 | semidirect |
| 4. #31826808 | C2 | semidirect |
| 5. #31826755 | C2 | semidirect |
| 6. #31826693 | C2 | semidirect |
| 7. #31826670 | C2 | semidirect |
| 8. #31826607 | C2 | semidirect |
| 9. C8×D1132 | C2 | semidirect |
| 10. #31826458 | C2 | semidirect |
| 11. C4×D8×C283 | C2 | semidirect |
| 130. C283 | #3303 | semidirect |
| 140. C4×D8 | D283 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31827180 | 2 |
| #31827119 | 2 |
| #31826816 | 2 |
| #31826808 | 2 |
| #31826755 | 2 |
| #31826693 | 2 |
| #31826670 | 2 |
| #31826607 | 2 |
| C8×D1132 | 2 |
| #31826458 | 2 |
| C4×D8×C283 | 2 |
| #3303 | 283 |