Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
384 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 384 conjugacy classes of subgroups — too many to draw. Only its 141 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. #30632054 | C2 | direct (N × H) |
| 96. C2×C251 | #491 | semidirect |
| 100. C251 | C2×#491 | semidirect |
| 197. C2 | #30632054 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22548713 | 2 |
| C2×#22548706 | 2 |
| #30632054 | 2 |
| C2×#22548640 | 2 |
| C2×#22548639 | 2 |
| C2×#22548638 | 2 |
| C2×#22548625 | 2 |
| C2×#103×C251 | 2 |
| C2×#491 | 251 |