Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
328 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 328 conjugacy classes of subgroups — too many to draw. Only its 125 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. #30631413 | C2 | direct (N × H) |
| 24. C22×C4×C251 | C8 | semidirect |
| 54. C2×C4×C251 | C2×C8 | semidirect |
| 76. C2×C251 | #324 | semidirect |
| 80. C251 | C2×#324 | semidirect |
| 103. C22×C4 | C251⋊C8 | semidirect |
| 134. C2×C4 | C2×C251⋊C8 | semidirect |
| 157. C2 | #30631413 | direct (N × H) |
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 |
| C22×C4⋊C4×C251 | 2 |
| C2×#324 | 251 |