Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
280 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 280 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 |
|---|---|---|
| 7. #22548649 | C4 | direct (N × H) |
| 12. C4×C8×C251 | C4 | semidirect |
| 40. C8×C251 | C42 | semidirect |
| 47. C4×C251 | #107 | semidirect |
| 57. C251 | C4×#107 | semidirect |
| 69. C4×C8 | Dic251 | semidirect |
| 98. C8 | C4×Dic251 | semidirect |
| 106. C4 | #22548649 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22548649 | 2 |
| C4×C4⋊Dic251 | 2 |
| #30631450 | 2 |
| C2×C4×C8×C251 | 2 |
| C4×#107 | 251 |