Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
362 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 362 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 |
|---|---|---|
| 1. #30632162 | C2 | semidirect |
| 2. #30631704 | C2 | semidirect |
| 3. C2×#22548632 | C2 | semidirect |
| 4. #30631443 | C2 | semidirect |
| 14. #127×C251 | C4 | semidirect |
| 15. #124×C251 | C4 | semidirect |
| 26. C4×Dic251 | D4 | semidirect |
| 30. C2×Q8×C251 | C2×C4 | semidirect |
| 36. C2×D4×C251 | C2×C4 | semidirect |
| 43. C42×C251 | C2×C4 | semidirect |
| 88. C251 | #1911 | semidirect |
| 98. #127 | Dic251 | semidirect |
| 99. #124 | Dic251 | semidirect |
| 111. C2×Q8 | C2×Dic251 | semidirect |
| 117. C2×D4 | C2×Dic251 | semidirect |
| 132. 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 |
| #30631704 | 2 |
| C2×#22548632 | 2 |
| #30631443 | 2 |
| #535×C251 | 2 |
| #1911 | 251 |