Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
298 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 298 conjugacy classes of subgroups — too many to draw. Only its 101 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 |
|---|---|---|
| 19. #22548638 | C4 | semidirect |
| 57. Dic502 | C4⋊C4 | semidirect |
| 109. C251 | #1865 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22548680 | 2 |
| C2×#22548646 | 2 |
| C2×#22548640 | 2 |
| C2×#22548638 | 2 |
| #30631586 | 2 |
| #30631441 | 2 |
| #340×C251 | 2 |
| #1865 | 251 |