Finite Group DatabasebetaFinite Group DatabasebetaOrder 36224.
362 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 362 conjugacy classes of subgroups — too many to draw. Only its 125 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. #31827200 | C2 | semidirect |
| 2. #31826822 | C2 | semidirect |
| 3. #31826813 | C2 | semidirect |
| 4. #31826762 | C2 | semidirect |
| 5. #31826757 | C2 | semidirect |
| 6. #31826680 | C2 | semidirect |
| 8. Q8×C283⋊C8 | C2 | semidirect |
| 9. C4×#17985380 | C2 | semidirect |
| 10. C4×#17985377 | C2 | semidirect |
| 11. #554×C283 | C2 | semidirect |
| 122. C283 | #3361 | semidirect |
| 125. #554 | D283 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31827200 | 2 |
| #31826822 | 2 |
| #31826813 | 2 |
| #31826762 | 2 |
| #31826757 | 2 |
| #31826680 | 2 |
| #31826660 | 2 |
| Q8×C283⋊C8 | 2 |
| C4×#17985380 | 2 |
| C4×#17985377 | 2 |
| #554×C283 | 2 |
| #3361 | 283 |