Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
340 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 340 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 |
|---|---|---|
| 1. #30632454 | C2 | semidirect |
| 3. C2×#22548631 | C2 | semidirect |
| 4. #30631458 | C2 | semidirect |
| 5. #413×C251 | C2 | semidirect |
| 28. #16860794 | D4 | semidirect |
| 85. C251 | #1914 | semidirect |
| 89. #413 | D251 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #30632454 | 2 |
| #30632251 | 2 |
| C2×#22548631 | 2 |
| #30631458 | 2 |
| #413×C251 | 2 |
| #1914 | 251 |