Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
726 conjugacy classes of subgroups; only the 293 normal subgroups are shown.
This group has 726 conjugacy classes of subgroups — too many to draw. Only its 293 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×#22548722 | C2 | semidirect |
| 2. #30632170 | C2 | semidirect |
| 3. #30631696 | C2 | semidirect |
| 4. #30631688 | C2 | semidirect |
| 5. #30631683 | C2 | semidirect |
| 6. C2×#22548639 | C2 | semidirect |
| 21. 2−1+4×C251 | C4 | semidirect |
| 40. #41×C251 | C2×C4 | semidirect |
| 45. C2×Q8×C251 | C2×C4 | semidirect |
| 94. C251 | #2898 | semidirect |
| 104. 2−1+4 | Dic251 | semidirect |
| 125. #41 | C2×Dic251 | semidirect |
| 130. C2×Q8 | C2×Dic251 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22548722 | 2 |
| #30632170 | 2 |
| #30631696 | 2 |
| #30631688 | 2 |
| #30631683 | 2 |
| C2×#22548639 | 2 |
| C2×2−1+4×C251 | 2 |
| #2898 | 251 |