Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
408 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 408 conjugacy classes of subgroups — too many to draw. Only its 121 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. C22×#16860794 | C2 | semidirect |
| 2. C2×C22⋊(C251⋊C8) | C2 | semidirect |
| 3. C2×C22⋊(C251⋊C8) | C2 | semidirect |
| 4. #30631442 | C2 | semidirect |
| 27. C2×C251⋊C8 | D4 | semidirect |
| 62. C23×C251 | M16 | semidirect |
| 79. C2×C4×C251 | M16 | semidirect |
| 113. C251 | #1870 | semidirect |
| 174. C23 | #16860794 | semidirect |
| 191. C2×C4 | #16860794 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#16860794 | 2 |
| C2×C22⋊(C251⋊C8) | 2 |
| #30631442 | 2 |
| C2×C4×D4×C251 | 2 |
| #1870 | 251 |