Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
360 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 165 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 |
|---|---|---|
| 2. #30632088 | C2 | direct (N × H) |
| 63. C2×C251 | #499 | semidirect |
| 67. C251 | C2×#499 | semidirect |
| 131. C2 | #30632088 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22548706 | 2 |
| #30632088 | 2 |
| C2×#22548649 | 2 |
| C2×#22548646 | 2 |
| C2×C8×Dic251 | 2 |
| C2×#107×C251 | 2 |
| C2×#499 | 251 |