Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
360 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 125 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×#22548646 | C2 | semidirect |
| 4. #30631449 | C2 | semidirect |
| 11. C22⋊(C251⋊C8) | C4 | semidirect |
| 22. C2×C251⋊C8 | C2×C4 | semidirect |
| 74. C22×C251 | #106 | semidirect |
| 96. C251 | #1853 | semidirect |
| 171. C22 | #22548646 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22548646 | 2 |
| C2×C22⋊(C251⋊C8) | 2 |
| #30631547 | 2 |
| #30631449 | 2 |
| C22×C4⋊C4×C251 | 2 |
| #1853 | 251 |