Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
376 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 376 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. C2×#22548641 | C2 | semidirect |
| 3. C4×C22⋊Dic251 | C2 | semidirect |
| 4. #30631448 | C2 | semidirect |
| 5. C22×M16×C251 | C2 | semidirect |
| 8. #22548694 | C4 | semidirect |
| 9. #22548694 | C4 | semidirect |
| 10. #22548689 | C4 | semidirect |
| 11. #22548689 | C4 | semidirect |
| 58. M16×C251 | D4 | semidirect |
| 103. C22×C251 | #104 | semidirect |
| 125. C251 | #1871 | semidirect |
| 127. C22×M16 | D251 | semidirect |
| 171. M16 | C22⋊D251 | semidirect |
| 232. C22 | #22548641 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #30632198 | 2 |
| C2×#22548641 | 2 |
| C4×C22⋊Dic251 | 2 |
| #30631448 | 2 |
| C22×M16×C251 | 2 |
| #1871 | 251 |