Finite Group DatabasebetaFinite Group DatabasebetaOrder 32192.
218 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 218 conjugacy classes of subgroups — too many to draw. Only its 93 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 | #126×C503 | C2 |
| prime radical | #30632837 | C2 |
| hypercenter | #126 | D503 |
| hypocenter | C503 | #539 |
| LCS | G ▷ C22×C503 ▷ C503 | |
| UCS | C1 ◁ C22 ◁ #126 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #30632859 | C2 | semidirect |
| 2. #30632856 | C2 | semidirect |
| 3. #30632855 | C2 | semidirect |
| 4. #30632849 | C2 | semidirect |
| 5. #30632848 | C2 | semidirect |
| 6. #30632846 | C2 | semidirect |
| 7. #30632846 | C2 | semidirect |
| 8. #30632844 | C2 | semidirect |
| 9. #30632842 | C2 | semidirect |
| 10. #30632841 | C2 | semidirect |
| 12. C4×D2012 | C2 | semidirect |
| 13. (C22⋊D503)⋊C4 | C2 | semidirect |
| 14. C4⋊C4×D503 | C2 | semidirect |
| 15. #126×C503 | C2 | semidirect |
| 103. C503 | #539 | semidirect |
| 106. #126 | D503 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #30632859 | 2 |
| #30632856 | 2 |
| #30632855 | 2 |
| #30632849 | 2 |
| #30632848 | 2 |
| #30632846 | 2 |
| #30632844 | 2 |
| #30632842 | 2 |
| #30632841 | 2 |
| #30632837 | 2 |
| C4×D2012 | 2 |
| (C22⋊D503)⋊C4 | 2 |
| C4⋊C4×D503 | 2 |
| #126×C503 | 2 |
| #539 | 503 |