Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
700 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 700 conjugacy classes of subgroups — too many to draw. Only its 165 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×#22548745 | C2 | semidirect |
| 2. C22×#16860800 | C2 | semidirect |
| 3. #30632258 | C2 | semidirect |
| 4. #30631849 | C2 | semidirect |
| 5. #30631843 | C2 | semidirect |
| 6. #30631696 | C2 | semidirect |
| 7. #30631683 | C2 | semidirect |
| 8. #30631654 | C2 | semidirect |
| 140. C251 | #3011 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22548745 | 2 |
| C22×#16860800 | 2 |
| #30632258 | 2 |
| #30631849 | 2 |
| #30631843 | 2 |
| #30631696 | 2 |
| #30631683 | 2 |
| #30631654 | 2 |
| C2×2−1+4×C251 | 2 |
| #3011 | 251 |