Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
374 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 374 conjugacy classes of subgroups — too many to draw. Only its 107 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×Q8×Dic251 | C2 | semidirect |
| 5. #30631449 | C2 | semidirect |
| 6. #30631441 | C2 | semidirect |
| 7. C2×#103×C251 | C2 | semidirect |
| 11. C2×#16860797 | C4 | semidirect |
| 81. C2×Dic251 | SD16 | semidirect |
| 87. Q8×C251 | C22⋊C4 | semidirect |
| 132. C251 | #1880 | semidirect |
| 136. C2×#103 | D251 | semidirect |
| 206. Q8 | (C2×D251)⋊C4 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#16860797 | 2 |
| C2×Q8×Dic251 | 2 |
| C2×#22548637 | 2 |
| #30631588 | 2 |
| #30631449 | 2 |
| #30631441 | 2 |
| C2×#103×C251 | 2 |
| #1880 | 251 |