Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
332 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 332 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×C22⋊(C251⋊C8) | C2 | semidirect |
| 2. #30631413 | C2 | semidirect |
| 3. #30631411 | C2 | semidirect |
| 23. C2×D4×C251 | C8 | semidirect |
| 49. C23×C251 | C2×C8 | semidirect |
| 67. C2×C4×C251 | C2×C8 | semidirect |
| 97. C251 | #1459 | semidirect |
| 119. C2×D4 | C251⋊C8 | semidirect |
| 146. C23 | C2×C251⋊C8 | semidirect |
| 164. C2×C4 | C2×C251⋊C8 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C22⋊(C251⋊C8) | 2 |
| #30631413 | 2 |
| #30631411 | 2 |
| C2×C4×D4×C251 | 2 |
| #1459 | 251 |