Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
612 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 612 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×C22⋊(C251⋊C8) | C2 | semidirect |
| 3. C2×(C2×D251)⋊C8 | C2 | semidirect |
| 4. C2×C22⋊C8×C251 | C2 | semidirect |
| 93. C251 | #1780 | semidirect |
| 98. C2×C22⋊C8 | D251 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#16860810 | 2 |
| C2×C22⋊(C251⋊C8) | 2 |
| C2×(C2×D251)⋊C8 | 2 |
| C2×C22⋊C8×C251 | 2 |
| #1780 | 251 |