Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
348 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 348 conjugacy classes of subgroups — too many to draw. Only its 117 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 |
|---|---|---|
| 2. C2×Dic251⋊C8 | C2 | semidirect |
| 5. #30631442 | C2 | semidirect |
| 6. #30631441 | C2 | semidirect |
| 7. C2×C4⋊C8×C251 | C2 | semidirect |
| 43. (C2×D251)⋊C4 | C8 | semidirect |
| 72. C2×Dic251 | C2×C8 | semidirect |
| 85. C2×C4×C251 | C2×C8 | semidirect |
| 107. C2×D251 | C4⋊C8 | semidirect |
| 125. C251 | #1850 | semidirect |
| 129. C2×C4⋊C8 | D251 | semidirect |
| 209. C2×C4 | C8×D251 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C8×D251 | 2 |
| C2×Dic251⋊C8 | 2 |
| C2×(C2×D251)⋊C8 | 2 |
| C4×(C2×D251)⋊C4 | 2 |
| #30631442 | 2 |
| #30631441 | 2 |
| C2×C4⋊C8×C251 | 2 |
| #1850 | 251 |