Finite Group DatabasebetaFinite Group DatabasebetaOrder 32192.
234 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 234 conjugacy classes of subgroups — too many to draw. Only its 101 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. #30632859 | C2 | semidirect |
| 2. #30632855 | C2 | semidirect |
| 3. #30632853 | C2 | semidirect |
| 4. #30632849 | C2 | semidirect |
| 5. #30632840 | C2 | semidirect |
| 7. C4×D2012 | C2 | semidirect |
| 8. C4×D2012 | C2 | semidirect |
| 9. #30632821 | C2 | semidirect |
| 10. C42×D503 | C2 | semidirect |
| 11. C4×Q8×C503 | C2 | semidirect |
| 74. C503 | #529 | semidirect |
| 82. C4×Q8 | D503 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #30632859 | 2 |
| #30632855 | 2 |
| #30632853 | 2 |
| #30632849 | 2 |
| #30632840 | 2 |
| #30632839 | 2 |
| C4×D2012 | 2 |
| #30632821 | 2 |
| C42×D503 | 2 |
| C4×Q8×C503 | 2 |
| #529 | 503 |