Finite Group DatabasebetaFinite Group DatabasebetaOrder 32192.
248 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 248 conjugacy classes of subgroups — too many to draw. Only its 99 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. #30632912 | C2 | semidirect |
| 2. #30632911 | C2 | semidirect |
| 3. #30632897 | C2 | semidirect |
| 4. #30632896 | C2 | semidirect |
| 5. #30632893 | C2 | semidirect |
| 6. #30632885 | C2 | semidirect |
| 7. #30632884 | C2 | semidirect |
| 8. C2×#22548873 | C2 | semidirect |
| 9. Q16×D503 | C2 | semidirect |
| 10. #30632872 | C2 | semidirect |
| 11. #137×C503 | C2 | semidirect |
| 87. C503 | #578 | semidirect |
| 94. #137 | D503 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #30632912 | 2 |
| #30632911 | 2 |
| #30632897 | 2 |
| #30632896 | 2 |
| #30632893 | 2 |
| #30632885 | 2 |
| #30632884 | 2 |
| C2×#22548873 | 2 |
| Q16×D503 | 2 |
| #30632872 | 2 |
| #137×C503 | 2 |
| #578 | 503 |