Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
618 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 618 conjugacy classes of subgroups — too many to draw. Only its 129 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. C2×#22548642 | C2 | semidirect |
| 2. #30631651 | C2 | semidirect |
| 3. C4×C22⋊Dic251 | C2 | semidirect |
| 5. C2×#16860794 | C22 | semidirect |
| 7. C2×C4×Dic251 | C22 | semidirect |
| 15. C2×#41×C251 | C4 | semidirect |
| 17. C22×Q8×C251 | C4 | semidirect |
| 19. C22×D4×C251 | C4 | semidirect |
| 71. Q8×C251 | C22⋊C4 | semidirect |
| 76. D4×C251 | C22⋊C4 | semidirect |
| 103. C22×C251 | #104 | semidirect |
| 119. C251 | #1789 | semidirect |
| 128. C2×#41 | Dic251 | semidirect |
| 130. C22×Q8 | Dic251 | semidirect |
| 132. C22×D4 | Dic251 | semidirect |
| 187. Q8 | C22⋊Dic251 | semidirect |
| 192. D4 | C22⋊Dic251 | semidirect |
| 223. C22 | #22548642 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22548642 | 2 |
| #30631651 | 2 |
| C4×C22⋊Dic251 | 2 |
| C22×#41×C251 | 2 |
| #1789 | 251 |