Finite Group DatabasebetaFinite Group DatabasebetaOrder 38336.
196 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 196 conjugacy classes of subgroups — too many to draw. Only its 91 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. #34062714 | C2 | semidirect |
| 2. #34062713 | C2 | semidirect |
| 3. #34062710 | C2 | semidirect |
| 4. #34062710 | C2 | semidirect |
| 5. #34062708 | C2 | semidirect |
| 6. #34062708 | C2 | semidirect |
| 7. #34062706 | C2 | semidirect |
| 8. #34062705 | C2 | semidirect |
| 12. #34062694 | C2 | semidirect |
| 13. #34062693 | C2 | semidirect |
| 14. #34062691 | C2 | semidirect |
| 15. C22⋊Q8×C599 | C2 | semidirect |
| 97. C599 | #563 | semidirect |
| 113. C22⋊Q8 | D599 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #34062714 | 2 |
| #34062713 | 2 |
| #34062710 | 2 |
| #34062708 | 2 |
| #34062706 | 2 |
| #34062705 | 2 |
| #34062701 | 2 |
| #34062698 | 2 |
| #34062697 | 2 |
| #34062694 | 2 |
| #34062693 | 2 |
| #34062691 | 2 |
| C22⋊Q8×C599 | 2 |
| #563 | 599 |