Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
362 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 362 conjugacy classes of subgroups — too many to draw. Only its 103 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. C2×#22548647 | C2 | semidirect |
| 5. #30631585 | C2 | semidirect |
| 6. #30631450 | C2 | semidirect |
| 7. #336×C251 | C2 | semidirect |
| 19. #22548637 | C4 | semidirect |
| 41. C4⋊Dic251 | C2×C4 | semidirect |
| 53. C2×C8×C251 | C2×C4 | semidirect |
| 66. D1004 | C4⋊C4 | semidirect |
| 123. C251 | #1864 | semidirect |
| 131. #336 | D251 | semidirect |
| 169. 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×C4×D1004 | 2 |
| C2×#22548647 | 2 |
| C2×#22548637 | 2 |
| #30631585 | 2 |
| #30631450 | 2 |
| #336×C251 | 2 |
| #1864 | 251 |