Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
164 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 164 conjugacy classes of subgroups — too many to draw. Only its 87 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×#22548655 | C2 | semidirect |
| 2. C22×C251⋊C16 | C2 | semidirect |
| 3. C4⋊(C251⋊C16) | C2 | semidirect |
| 4. C22⋊(C251⋊C16) | C2 | semidirect |
| 5. C22⋊(C251⋊C16) | C2 | semidirect |
| 6. #30631463 | C2 | semidirect |
| 24. C251⋊C16 | D4 | semidirect |
| 62. C22×C251 | M32 | semidirect |
| 75. C251 | #2168 | semidirect |
| 138. C22 | #22548655 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22548655 | 2 |
| C22×C251⋊C16 | 2 |
| C4⋊(C251⋊C16) | 2 |
| C22⋊(C251⋊C16) | 2 |
| #30631463 | 2 |
| C8×D4×C251 | 2 |
| #2168 | 251 |