Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
154 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 154 conjugacy classes of subgroups — too many to draw. Only its 57 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 |
|---|---|---|
| 49. C4×C251 | Q32 | semidirect |
| 56. C251 | #2209 | semidirect |
| 107. C4 | #22548661 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22548661 | 2 |
| #30632067 | 2 |
| C4⋊(C251⋊C16) | 2 |
| #30631490 | 2 |
| C4×Q16×C251 | 2 |
| #2209 | 251 |