Finite Group DatabasebetaFinite Group DatabasebetaOrder 36224.
386 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 386 conjugacy classes of subgroups — too many to draw. Only its 115 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. #31827189 | C2 | semidirect |
| 3. #31826804 | C2 | semidirect |
| 4. #31826742 | C2 | semidirect |
| 5. #31826705 | C2 | semidirect |
| 6. #31826672 | C2 | semidirect |
| 7. #31826630 | C2 | semidirect |
| 8. C4×#17985381 | C2 | semidirect |
| 9. C8×D1132 | C2 | semidirect |
| 10. #31826460 | C2 | semidirect |
| 11. #487×C283 | C2 | semidirect |
| 125. C283 | #3302 | semidirect |
| 129. #487 | D283 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31827189 | 2 |
| #31827118 | 2 |
| #31826804 | 2 |
| #31826742 | 2 |
| #31826705 | 2 |
| #31826672 | 2 |
| #31826630 | 2 |
| C4×#17985381 | 2 |
| C8×D1132 | 2 |
| #31826460 | 2 |
| #487×C283 | 2 |
| #3302 | 283 |