Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
500 conjugacy classes of subgroups; only the 185 normal subgroups are shown.
This group has 500 conjugacy classes of subgroups — too many to draw. Only its 185 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. #30632155 | C2 | semidirect |
| 3. #30631781 | C2 | semidirect |
| 4. #30631774 | C2 | semidirect |
| 5. #30631769 | C2 | semidirect |
| 6. #30631681 | C2 | semidirect |
| 7. C2×C8×Dic251 | C2 | semidirect |
| 8. #427×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 |
| 49. C2×C8×C251 | C2×C4 | semidirect |
| 87. Dic251 | #135 | semidirect |
| 92. C251 | C4×#135 | semidirect |
| 99. #427 | D251 | semidirect |
| 136. 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 |
| #30632155 | 2 |
| #30631781 | 2 |
| #30631774 | 2 |
| #30631769 | 2 |
| #30631681 | 2 |
| C2×C8×Dic251 | 2 |
| #427×C251 | 2 |
| C4×#135 | 251 |