Finite Group DatabasebetaFinite Group DatabasebetaOrder 32192.
220 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 220 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.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C23×D503 |
| commutator, socle, cosocle | C22×C503 | C24 |
| Fitting | C22⋊Q8×C503 | C2 |
| hypercenter | C22⋊Q8 | D503 |
| hypocenter | C503 | #562 |
| LCS | G ▷ C22×C503 ▷ C503 | |
| UCS | C1 ◁ C22 ◁ C22⋊Q8 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #30632854 | C2 | semidirect |
| 2. #30632853 | C2 | semidirect |
| 3. #30632850 | C2 | semidirect |
| 4. #30632849 | C2 | semidirect |
| 5. #30632849 | C2 | semidirect |
| 6. #30632847 | C2 | semidirect |
| 7. #30632846 | C2 | semidirect |
| 8. #30632844 | C2 | semidirect |
| 9. #30632842 | C2 | semidirect |
| 10. #30632840 | C2 | semidirect |
| 11. #30632839 | C2 | semidirect |
| 12. #30632838 | C2 | semidirect |
| 13. #30632837 | C2 | semidirect |
| 14. #30632837 | C2 | semidirect |
| 15. C22⋊Q8×C503 | C2 | semidirect |
| 109. C503 | #562 | semidirect |
| 121. C22⋊Q8 | D503 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #30632854 | 2 |
| #30632853 | 2 |
| #30632850 | 2 |
| #30632849 | 2 |
| #30632847 | 2 |
| #30632846 | 2 |
| #30632844 | 2 |
| #30632842 | 2 |
| #30632840 | 2 |
| #30632839 | 2 |
| #30632838 | 2 |
| #30632837 | 2 |
| C22⋊Q8×C503 | 2 |
| #562 | 503 |