Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
996 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 996 conjugacy classes of subgroups — too many to draw. Only its 181 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. C22×#16860797 | C2 | semidirect |
| 3. #30631837 | C2 | direct (N × H) |
| 4. C2×#22548635 | C2 | semidirect |
| 5. C2×C22⋊(C251⋊C8) | C2 | semidirect |
| 6. C2×C22⋊Q8×C251 | C2 | semidirect |
| 14. C2×#16860797 | C22 | semidirect |
| 15. C22×C251⋊C8 | C22 | semidirect |
| 16. #22548635 | C22 | semidirect |
| 17. C22⋊(C251⋊C8) | C22 | semidirect |
| 18. C22×Q8×C251 | C22 | semidirect |
| 21. C22⋊Q8×C251 | C22 | semidirect |
| 23. C2×C4⋊C4×C251 | C22 | semidirect |
| 40. C2×C251⋊C8 | C23 | semidirect |
| 44. C2×Q8×C251 | C23 | semidirect |
| 54. C4⋊C4×C251 | C23 | semidirect |
| 71. C23×C251 | SD16 | semidirect |
| 92. C22×C251 | C2×SD16 | semidirect |
| 106. C2×C251 | #450 | semidirect |
| 111. C251 | C2×#450 | semidirect |
| 115. C2×C22⋊Q8 | D251 | semidirect |
| 120. C22×Q8 | C2×D251 | semidirect |
| 131. C22⋊Q8 | C2×D251 | semidirect |
| 133. C2×C4⋊C4 | C2×D251 | semidirect |
| 145. C2×Q8 | C22×D251 | semidirect |
| 166. C4⋊C4 | C22×D251 | semidirect |
| 178. C23 | #16860797 | semidirect |
| 209. C22 | C2×#16860797 | semidirect |
| 219. C2 | #30631837 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×D1004 | 2 |
| C22×#16860797 | 2 |
| #30631837 | 2 |
| C2×#22548635 | 2 |
| C2×C22⋊(C251⋊C8) | 2 |
| C2×C22⋊Q8×C251 | 2 |
| C2×#450 | 251 |