Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
484 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 484 conjugacy classes of subgroups — too many to draw. Only its 145 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×#22548748 | C2 | semidirect |
| 3. C2×C4×Dic502 | C2 | semidirect |
| 4. #30631910 | C2 | semidirect |
| 5. #30631898 | C2 | semidirect |
| 6. #30631888 | C2 | semidirect |
| 7. #30631689 | C2 | semidirect |
| 8. #423×C251 | C2 | semidirect |
| 38. C2×Dic502 | D4 | semidirect |
| 109. C4×C251 | #137 | semidirect |
| 120. C251 | #3037 | semidirect |
| 128. #423 | D251 | semidirect |
| 233. C4 | #22548748 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22548748 | 2 |
| #30632237 | 2 |
| C2×C4×Dic502 | 2 |
| #30631910 | 2 |
| #30631898 | 2 |
| #30631888 | 2 |
| #30631689 | 2 |
| #423×C251 | 2 |
| #3037 | 251 |