Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
556 conjugacy classes of subgroups; only the 189 normal subgroups are shown.
This group has 556 conjugacy classes of subgroups — too many to draw. Only its 189 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. C2×#22548707 | C2 | semidirect |
| 2. #30631585 | C2 | semidirect |
| 3. #30631571 | C2 | semidirect |
| 5. #30631553 | C2 | semidirect |
| 74. C22×C251 | #125 | semidirect |
| 92. C251 | #2851 | semidirect |
| 167. C22 | #22548707 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22548707 | 2 |
| #30631585 | 2 |
| #30631571 | 2 |
| #30631560 | 2 |
| #30631553 | 2 |
| #30631547 | 2 |
| C22×C42×C251 | 2 |
| #2851 | 251 |