Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
484 conjugacy classes of subgroups; only the 221 normal subgroups are shown.
This group has 484 conjugacy classes of subgroups — too many to draw. Only its 221 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. #30632170 | C2 | semidirect |
| 2. #30631788 | C2 | semidirect |
| 3. Q16×Dic251 | C2 | semidirect |
| 4. D8×Dic251 | C2 | semidirect |
| 5. C2×#22548649 | C2 | semidirect |
| 6. #30631688 | C2 | semidirect |
| 7. #30631642 | C2 | semidirect |
| 24. #135×C251 | C4 | semidirect |
| 43. #41×C251 | C2×C4 | semidirect |
| 49. Q16×C251 | C2×C4 | semidirect |
| 50. SD16×C251 | C2×C4 | semidirect |
| 51. D8×C251 | C2×C4 | semidirect |
| 52. C2×C8×C251 | C2×C4 | semidirect |
| 95. C251 | #2951 | semidirect |
| 106. #135 | Dic251 | semidirect |
| 126. #41 | C2×Dic251 | semidirect |
| 134. Q16 | C2×Dic251 | semidirect |
| 135. SD16 | C2×Dic251 | semidirect |
| 136. D8 | C2×Dic251 | semidirect |
| 139. C2×C8 | C2×Dic251 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #30632170 | 2 |
| #30631788 | 2 |
| Q16×Dic251 | 2 |
| D8×Dic251 | 2 |
| C2×#22548649 | 2 |
| #30631688 | 2 |
| #30631642 | 2 |
| C2×#135×C251 | 2 |
| #2951 | 251 |