Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
276 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 276 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 |
|---|---|---|
| 1. #30631740 | C2 | semidirect |
| 2. C2×C4×C251⋊C8 | C2 | semidirect |
| 3. Q8⋊(C251⋊C8) | C2 | semidirect |
| 4. D4⋊(C251⋊C8) | C2 | semidirect |
| 27. #41×C251 | C8 | semidirect |
| 56. Q8×C251 | C2×C8 | semidirect |
| 59. D4×C251 | C2×C8 | semidirect |
| 98. C251 | #1476 | semidirect |
| 123. #41 | C251⋊C8 | semidirect |
| 153. Q8 | C2×C251⋊C8 | semidirect |
| 156. D4 | C2×C251⋊C8 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #30631740 | 2 |
| C2×C4×C251⋊C8 | 2 |
| Q8⋊(C251⋊C8) | 2 |
| D4⋊(C251⋊C8) | 2 |
| C4×#41×C251 | 2 |
| #1476 | 251 |