Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
360 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 97 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. #30631696 | C2 | semidirect |
| 4. #30631447 | C2 | semidirect |
| 15. #124×C251 | C4 | semidirect |
| 30. C2×Q8×C251 | C2×C4 | semidirect |
| 40. C42×C251 | C2×C4 | semidirect |
| 80. C251 | #1885 | semidirect |
| 91. #124 | Dic251 | semidirect |
| 103. C2×Q8 | C2×Dic251 | semidirect |
| 121. C42 | C2×Dic251 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #30632162 | 2 |
| #30631696 | 2 |
| C2×#22548632 | 2 |
| #30631447 | 2 |
| C2×#124×C251 | 2 |
| #1885 | 251 |