Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
172 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 172 conjugacy classes of subgroups — too many to draw. Only its 89 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 |
|---|---|---|
| 15. #97×C251 | C4 | semidirect |
| 16. C4×C8×C251 | C4 | semidirect |
| 65. C251 | #1833 | semidirect |
| 81. #97 | Dic251 | semidirect |
| 82. C4×C8 | Dic251 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22548651 | 2 |
| #30631725 | 2 |
| #30631458 | 2 |
| #30631443 | 2 |
| #405×C251 | 2 |
| #1833 | 251 |