Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
484 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 484 conjugacy classes of subgroups — too many to draw. Only its 181 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. #30632168 | C2 | semidirect |
| 3. #30631798 | C2 | semidirect |
| 4. #30631793 | C2 | semidirect |
| 5. #30631774 | C2 | semidirect |
| 6. #30631686 | C2 | semidirect |
| 7. #30631642 | C2 | semidirect |
| 8. C2×#106×C251 | C2 | semidirect |
| 10. #22548737 | C4 | semidirect |
| 30. #16860810 | C2×C4 | semidirect |
| 36. Dic1004 | C2×C4 | semidirect |
| 37. #16860799 | C2×C4 | semidirect |
| 38. D2008 | C2×C4 | semidirect |
| 49. C2×C8×C251 | C2×C4 | semidirect |
| 90. C251 | #2952 | semidirect |
| 97. C2×#106 | D251 | semidirect |
| 134. 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 |
| #30632168 | 2 |
| #30631798 | 2 |
| #30631793 | 2 |
| #30631774 | 2 |
| #30631686 | 2 |
| #30631642 | 2 |
| C2×#106×C251 | 2 |
| #2952 | 251 |