Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
656 conjugacy classes of subgroups; only the 197 normal subgroups are shown.
This group has 656 conjugacy classes of subgroups — too many to draw. Only its 197 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 |
|---|---|---|
| 1. C22×#16860797 | C2 | semidirect |
| 3. #30632061 | C2 | direct (N × H) |
| 4. C2×C4×C251⋊C8 | C2 | semidirect |
| 5. C2×C4⋊Q8×C251 | C2 | semidirect |
| 9. C2×#16860797 | C22 | semidirect |
| 13. C4×C251⋊C8 | C22 | semidirect |
| 16. C4⋊Q8×C251 | C22 | semidirect |
| 26. C2×C251⋊C8 | D4 | semidirect |
| 43. C251⋊C8 | C2×D4 | semidirect |
| 49. C2×C4×C251 | SD16 | semidirect |
| 62. C4×C251 | C2×SD16 | semidirect |
| 64. C2×C251 | #492 | semidirect |
| 68. C251 | C2×#492 | semidirect |
| 71. C2×C4⋊Q8 | D251 | semidirect |
| 82. C4⋊Q8 | C2×D251 | semidirect |
| 117. C2×C4 | #16860797 | semidirect |
| 131. C4 | C2×#16860797 | semidirect |
| 134. C2 | #30632061 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#16860797 | 2 |
| C2×#22548712 | 2 |
| #30632061 | 2 |
| C2×C4×C251⋊C8 | 2 |
| C2×C4⋊Q8×C251 | 2 |
| C2×#492 | 251 |