Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
428 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 428 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 |
|---|---|---|
| 2. C2×#22548637 | C2 | semidirect |
| 3. C4×C4⋊Dic251 | C2 | semidirect |
| 4. C2×C4⋊C8×C251 | C2 | semidirect |
| 9. #22548712 | C4 | semidirect |
| 29. C4⋊Dic251 | D4 | semidirect |
| 73. C4×C251 | #102 | semidirect |
| 84. C251 | #1982 | semidirect |
| 87. C2×C4⋊C8 | D251 | semidirect |
| 159. C4 | #22548637 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22548712 | 2 |
| C2×#22548637 | 2 |
| C4×C4⋊Dic251 | 2 |
| C2×C4⋊C8×C251 | 2 |
| #1982 | 251 |