Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
484 conjugacy classes of subgroups; only the 189 normal subgroups are shown.
This group has 484 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 |
|---|---|---|
| 2. #30632167 | C2 | semidirect |
| 3. #30631789 | C2 | semidirect |
| 4. C4×Dic1004 | C2 | semidirect |
| 5. C4×D2008 | C2 | semidirect |
| 6. C2×#22548649 | C2 | semidirect |
| 7. #30631689 | C2 | semidirect |
| 8. #405×C251 | C2 | semidirect |
| 10. #22548737 | C4 | semidirect |
| 30. #16860810 | C2×C4 | semidirect |
| 37. Dic1004 | C2×C4 | semidirect |
| 38. #16860799 | C2×C4 | semidirect |
| 39. D2008 | C2×C4 | semidirect |
| 47. C2×C8×C251 | C2×C4 | semidirect |
| 95. C251 | #2951 | semidirect |
| 104. #405 | D251 | semidirect |
| 138. C2×C8 | C4×D251 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22548737 | 2 |
| #30632167 | 2 |
| #30631789 | 2 |
| C4×Dic1004 | 2 |
| C4×D2008 | 2 |
| C2×#22548649 | 2 |
| #30631689 | 2 |
| #405×C251 | 2 |
| #2951 | 251 |