Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
216 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 61 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×#22548661 | C2 | semidirect |
| 3. #30631491 | C2 | semidirect |
| 53. C22×C251 | Q32 | semidirect |
| 65. C251 | #2188 | semidirect |
| 119. C22 | #22548661 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22548661 | 2 |
| #30631928 | 2 |
| #30631491 | 2 |
| C22⋊(C251⋊C16) | 2 |
| C22×Q16×C251 | 2 |
| #2188 | 251 |