Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
848 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 848 conjugacy classes of subgroups — too many to draw. Only its 157 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×#22548636 | C2 | semidirect |
| 2. C2×C22⋊(C251⋊C8) | C2 | semidirect |
| 3. #30631547 | C2 | semidirect |
| 5. C22×C251⋊C8 | C22 | semidirect |
| 6. C2×C4⋊Dic251 | C22 | semidirect |
| 15. C22×D4×C251 | C4 | semidirect |
| 66. D4×C251 | C22⋊C4 | semidirect |
| 84. C22×C251 | #102 | semidirect |
| 101. C251 | #1786 | semidirect |
| 111. C22×D4 | Dic251 | semidirect |
| 164. D4 | C22⋊Dic251 | semidirect |
| 186. C22 | #22548636 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22548636 | 2 |
| C2×C22⋊(C251⋊C8) | 2 |
| #30631547 | 2 |
| C23×D4×C251 | 2 |
| #1786 | 251 |