Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
552 conjugacy classes of subgroups; only the 221 normal subgroups are shown.
This group has 552 conjugacy classes of subgroups — too many to draw. Only its 221 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 |
|---|---|---|
| 3. C4×#16860797 | C2 | direct (N × H) |
| 4. C2×#22548646 | C2 | semidirect |
| 5. C2×#22548639 | C2 | semidirect |
| 7. C2×C4×C251⋊C8 | C2 | semidirect |
| 8. C2×C4×Q8×C251 | C2 | semidirect |
| 11. C2×#16860797 | C4 | direct (N × H) |
| 19. #22548646 | C22 | semidirect |
| 20. #22548639 | C22 | semidirect |
| 22. C4×C251⋊C8 | C22 | semidirect |
| 25. C4×Q8×C251 | C22 | semidirect |
| 38. #16860797 | C2×C4 | direct (N × H) |
| 40. C2×C251⋊C8 | C2×C4 | semidirect |
| 48. C2×Q8×C251 | C2×C4 | semidirect |
| 72. C251⋊C8 | C22×C4 | semidirect |
| 76. Q8×C251 | C22×C4 | semidirect |
| 82. C2×C4×C251 | SD16 | semidirect |
| 101. C4×C251 | C2×SD16 | semidirect |
| 105. C2×C251 | C4×SD16 | semidirect |
| 110. C251 | C2×C4×SD16 | semidirect |
| 113. C2×C4×Q8 | D251 | semidirect |
| 128. C4×Q8 | C2×D251 | semidirect |
| 144. C2×Q8 | C4×D251 | semidirect |
| 179. Q8 | C2×C4×D251 | semidirect |
| 191. C2×C4 | #16860797 | direct (N × H) |
| 213. C4 | C2×#16860797 | direct (N × H) |
| 217. C2 | C4×#16860797 | 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×C4×D1004 | 2 |
| C4×#16860797 | 2 |
| C2×#22548646 | 2 |
| C2×#22548639 | 2 |
| C2×#22548635 | 2 |
| C2×C4×C251⋊C8 | 2 |
| C2×C4×Q8×C251 | 2 |
| C2×C4×SD16 | 251 |