Finite Group DatabasebetaFinite Group DatabasebetaOrder 32192.
234 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 234 conjugacy classes of subgroups — too many to draw. Only its 103 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. #30632858 | C2 | semidirect |
| 2. #30632856 | C2 | semidirect |
| 3. #30632852 | C2 | semidirect |
| 4. #30632847 | C2 | semidirect |
| 5. #30632843 | C2 | semidirect |
| 7. C4×Dic1006 | C2 | semidirect |
| 8. C4×D2012 | C2 | semidirect |
| 9. C4×C22⋊D503 | C2 | semidirect |
| 10. #30632821 | C2 | semidirect |
| 11. C2×C42×C503 | C2 | semidirect |
| 74. C503 | #529 | semidirect |
| 86. C2×C42 | D503 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #30632858 | 2 |
| #30632856 | 2 |
| #30632852 | 2 |
| #30632847 | 2 |
| #30632843 | 2 |
| #30632838 | 2 |
| C4×Dic1006 | 2 |
| C4×D2012 | 2 |
| C4×C22⋊D503 | 2 |
| #30632821 | 2 |
| C2×C42×C503 | 2 |
| #529 | 503 |