Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
512 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 512 conjugacy classes of subgroups — too many to draw. Only its 165 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. C22×C4⋊Dic251 | C2 | semidirect |
| 2. #30632003 | C2 | direct (N × H) |
| 3. C2×#22548646 | C2 | semidirect |
| 4. C2×#22548636 | C2 | semidirect |
| 5. C2×C22⋊(C251⋊C8) | C2 | semidirect |
| 12. C2×C4⋊Dic251 | C22 | semidirect |
| 13. #22548646 | C22 | semidirect |
| 14. #22548636 | C22 | semidirect |
| 15. C22⋊(C251⋊C8) | C22 | semidirect |
| 91. C2×C251 | #481 | semidirect |
| 95. C251 | C2×#481 | semidirect |
| 187. C2 | #30632003 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C4⋊Dic251 | 2 |
| #30632003 | 2 |
| C2×#22548646 | 2 |
| C2×#22548636 | 2 |
| C2×C22⋊(C251⋊C8) | 2 |
| C2×#121×C251 | 2 |
| C2×#481 | 251 |