Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
256 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 256 conjugacy classes of subgroups — too many to draw. Only its 53 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×#22548658 | C2 | semidirect |
| 3. #30631925 | C2 | semidirect |
| 4. #30631489 | C2 | semidirect |
| 5. #30631488 | C2 | semidirect |
| 6. (C2×D251)⋊C16 | C2 | semidirect |
| 7. C2×SD32×C251 | C2 | semidirect |
| 16. C2×C251⋊C16 | C22 | semidirect |
| 17. #22548649 | C22 | semidirect |
| 19. C2×Q16×C251 | C22 | semidirect |
| 22. C2×C16×C251 | C22 | semidirect |
| 79. C2×D251 | SD32 | semidirect |
| 91. C251 | #2187 | semidirect |
| 95. C2×SD32 | D251 | semidirect |
| 101. C2×Q16 | C2×D251 | semidirect |
| 112. C2×C16 | C2×D251 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D8×D251 | 2 |
| C2×#22548658 | 2 |
| #30631925 | 2 |
| #30631489 | 2 |
| #30631488 | 2 |
| (C2×D251)⋊C16 | 2 |
| C2×SD32×C251 | 2 |
| #2187 | 251 |