Finite Group DatabasebetaFinite Group DatabasebetaOrder 32192.
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. #30632863 | C2 | semidirect |
| 2. #30632862 | C2 | semidirect |
| 3. #30632859 | C2 | semidirect |
| 4. #30632859 | C2 | semidirect |
| 5. #30632857 | C2 | semidirect |
| 6. #30632857 | C2 | semidirect |
| 7. #30632855 | C2 | semidirect |
| 8. #30632854 | C2 | semidirect |
| 12. #30632843 | C2 | semidirect |
| 13. #30632842 | C2 | semidirect |
| 14. #30632840 | C2 | semidirect |
| 15. C22⋊Q8×C503 | C2 | semidirect |
| 97. C503 | #563 | semidirect |
| 113. C22⋊Q8 | D503 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #30632863 | 2 |
| #30632862 | 2 |
| #30632859 | 2 |
| #30632857 | 2 |
| #30632855 | 2 |
| #30632854 | 2 |
| #30632850 | 2 |
| #30632847 | 2 |
| #30632846 | 2 |
| #30632843 | 2 |
| #30632842 | 2 |
| #30632840 | 2 |
| C22⋊Q8×C503 | 2 |
| #563 | 503 |