Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
344 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 344 conjugacy classes of subgroups — too many to draw. Only its 113 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×C4⋊(C251⋊C8) | C2 | semidirect |
| 2. C2×#22548639 | C2 | semidirect |
| 4. C4×C4⋊Dic251 | C2 | semidirect |
| 16. #124×C251 | C4 | semidirect |
| 94. C251 | #1983 | semidirect |
| 105. #124 | Dic251 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4⋊(C251⋊C8) | 2 |
| C2×#22548639 | 2 |
| C2×#22548636 | 2 |
| C4×C4⋊Dic251 | 2 |
| C2×#124×C251 | 2 |
| #1983 | 251 |