Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
670 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 670 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×#22548630 | C2 | semidirect |
| 2. #30631567 | C2 | semidirect |
| 4. C23×Dic251 | C22 | semidirect |
| 6. C2×C22⋊Dic251 | C22 | semidirect |
| 10. H(5,𝔽2)×C251 | C4 | semidirect |
| 49. C23×C251 | C22⋊C4 | semidirect |
| 60. C2×C4×C251 | C22⋊C4 | semidirect |
| 83. C251 | #1790 | semidirect |
| 89. H(5,𝔽2) | Dic251 | semidirect |
| 127. C23 | C22⋊Dic251 | semidirect |
| 144. C2×C4 | C22⋊Dic251 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22548630 | 2 |
| #30631567 | 2 |
| C2×H(5,𝔽2)×C251 | 2 |
| #1790 | 251 |