Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
338 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 338 conjugacy classes of subgroups — too many to draw. Only its 113 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 |
|---|---|---|
| 11. C2×#16860800 | C4 | semidirect |
| 88. C2×C4×C251 | Q16 | semidirect |
| 119. C251 | #1878 | semidirect |
| 206. C2×C4 | #16860800 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#16860800 | 2 |
| C2×#22548639 | 2 |
| C2×#22548638 | 2 |
| #30631593 | 2 |
| #30631449 | 2 |
| #30631442 | 2 |
| C2×C4×Q8×C251 | 2 |
| #1878 | 251 |