Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
336 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 336 conjugacy classes of subgroups — too many to draw. Only its 93 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×#22548643 | C2 | semidirect |
| 3. C4×#16860794 | C2 | semidirect |
| 4. C4×C4⋊C4×C251 | C2 | semidirect |
| 7. #22548715 | C4 | semidirect |
| 8. #22548712 | C4 | semidirect |
| 9. #22548703 | C4 | semidirect |
| 30. #16860794 | D4 | semidirect |
| 82. C4×C251 | #104 | semidirect |
| 92. C251 | #1980 | semidirect |
| 97. C4×C4⋊C4 | D251 | semidirect |
| 176. C4 | #22548643 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #30632237 | 2 |
| C2×#22548643 | 2 |
| C4×#16860794 | 2 |
| C4×C4⋊C4×C251 | 2 |
| #1980 | 251 |