Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
384 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 384 conjugacy classes of subgroups — too many to draw. Only its 149 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. #30631994 | C2 | semidirect |
| 3. #30631987 | C2 | semidirect |
| 4. #30631730 | C2 | semidirect |
| 5. #30631711 | C2 | semidirect |
| 90. C251 | #3080 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22548707 | 2 |
| #30631994 | 2 |
| #30631987 | 2 |
| #30631730 | 2 |
| #30631711 | 2 |
| #30631688 | 2 |
| C4×#41×C251 | 2 |
| #3080 | 251 |