Finite Group DatabasebetaFinite Group DatabasebetaOrder 36224.
350 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 350 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. #31827188 | C2 | semidirect |
| 2. #31827175 | C2 | semidirect |
| 3. #31826820 | C2 | semidirect |
| 4. #31826816 | C2 | semidirect |
| 5. #31826773 | C2 | semidirect |
| 6. #31826756 | C2 | semidirect |
| 8. #31826671 | C2 | semidirect |
| 9. C4×#17985381 | C2 | semidirect |
| 11. C8×Q8×C283 | C2 | semidirect |
| 120. C283 | #3360 | semidirect |
| 130. C8×Q8 | D283 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31827188 | 2 |
| #31827175 | 2 |
| #31826820 | 2 |
| #31826816 | 2 |
| #31826773 | 2 |
| #31826756 | 2 |
| #31826681 | 2 |
| #31826671 | 2 |
| C4×#17985381 | 2 |
| C4×D2264 | 2 |
| C8×Q8×C283 | 2 |
| #3360 | 283 |