Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
564 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 564 conjugacy classes of subgroups — too many to draw. Only its 137 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. C2×#22548736 | C2 | semidirect |
| 2. C2×#22548734 | C2 | semidirect |
| 3. #30632236 | C2 | semidirect |
| 4. #30632235 | C2 | semidirect |
| 5. #30632082 | C2 | semidirect |
| 6. #30632081 | C2 | semidirect |
| 7. #30632078 | C2 | semidirect |
| 8. #30632075 | C2 | semidirect |
| 9. #30632074 | C2 | semidirect |
| 10. #97×D251 | C2 | semidirect |
| 11. #496×C251 | C2 | semidirect |
| 64. C8×D251 | D4 | semidirect |
| 133. C251 | #3150 | semidirect |
| 144. #496 | D251 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22548736 | 2 |
| C2×#22548734 | 2 |
| #30632236 | 2 |
| #30632235 | 2 |
| #30632082 | 2 |
| #30632081 | 2 |
| #30632078 | 2 |
| #30632075 | 2 |
| #30632074 | 2 |
| #97×D251 | 2 |
| #496×C251 | 2 |
| #3150 | 251 |