Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
152 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 152 conjugacy classes of subgroups — too many to draw. Only its 85 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 |
|---|---|---|
| 3. #30631509 | C2 | direct (N × H) |
| 6. #22548655 | C4 | semidirect |
| 8. C2×C251⋊C16 | C4 | semidirect |
| 18. C251⋊C16 | C2×C4 | semidirect |
| 54. C2×C251 | #365 | semidirect |
| 56. C251 | C2×#365 | semidirect |
| 111. C2 | #30631509 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22548655 | 2 |
| C2×#22548651 | 2 |
| #30631509 | 2 |
| C2×#106×C251 | 2 |
| C2×#365 | 251 |