Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
360 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 360 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 |
|---|---|---|
| 2. C2×C4⋊(C251⋊C8) | C2 | semidirect |
| 3. #30631430 | C2 | direct (N × H) |
| 4. C2×C4⋊C8×C251 | C2 | semidirect |
| 14. C4⋊(C251⋊C8) | C22 | semidirect |
| 18. C4⋊C8×C251 | C22 | semidirect |
| 84. C2×C251 | #331 | semidirect |
| 89. C251 | C2×#331 | semidirect |
| 93. C2×C4⋊C8 | D251 | semidirect |
| 108. C4⋊C8 | C2×D251 | semidirect |
| 175. C2 | #30631430 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22548712 | 2 |
| C2×C4⋊(C251⋊C8) | 2 |
| #30631430 | 2 |
| C2×C4⋊C8×C251 | 2 |
| C2×#331 | 251 |