Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
384 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 384 conjugacy classes of subgroups — too many to draw. Only its 125 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 |
|---|---|---|
| 3. #30632057 | C2 | semidirect |
| 4. #30632056 | C2 | semidirect |
| 5. #30632055 | C2 | semidirect |
| 6. #30632054 | C2 | semidirect |
| 9. #491×C251 | C2 | semidirect |
| 86. D251 | #491 | direct (N × H) |
| 87. C251 | C2×#491 | semidirect |
| 95. #491 | D251 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4⋊Q8×D251 | 2 |
| #125×D251 | 2 |
| #30632057 | 2 |
| #30632056 | 2 |
| #30632055 | 2 |
| #30632054 | 2 |
| #103×D251 | 2 |
| #97×D251 | 2 |
| #491×C251 | 2 |
| C2×#491 | 251 |