Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
752 conjugacy classes of subgroups; only the 309 normal subgroups are shown.
This group has 752 conjugacy classes of subgroups — too many to draw. Only its 309 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. #30631696 | C2 | direct (N × H) |
| 4. C2×#22548639 | C2 | semidirect |
| 14. #22548639 | C22 | semidirect |
| 18. C22×Q8×C251 | C4 | semidirect |
| 39. C2×Q8×C251 | C2×C4 | semidirect |
| 86. C2×C251 | #419 | semidirect |
| 89. C251 | C2×#419 | semidirect |
| 99. C22×Q8 | Dic251 | semidirect |
| 121. C2×Q8 | C2×Dic251 | semidirect |
| 176. C2 | #30631696 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#16860794 | 2 |
| C2×#22548674 | 2 |
| #30631696 | 2 |
| C2×#22548639 | 2 |
| C23×Q8×C251 | 2 |
| C2×#419 | 251 |