Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
1464 conjugacy classes of subgroups; only the 525 normal subgroups are shown.
This group has 1464 conjugacy classes of subgroups — too many to draw. Only its 525 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×Q8×D251 | C2 | semidirect |
| 3. C2×#22548744 | C2 | direct (N × H) |
| 4. C22×Dic1004 | C2 | semidirect |
| 5. C22×#16860800 | C2 | semidirect |
| 6. C22×#16860798 | C2 | semidirect |
| 7. C22×#16860793 | C2 | semidirect |
| 8. C22×SD16×C251 | C2 | semidirect |
| 15. C2×Q8×D251 | C22 | semidirect |
| 20. #22548744 | C22 | direct (N × H) |
| 21. C2×Dic1004 | C22 | semidirect |
| 22. C2×#16860800 | C22 | semidirect |
| 23. C2×#16860798 | C22 | semidirect |
| 24. C2×#16860793 | C22 | semidirect |
| 28. C2×SD16×C251 | C22 | semidirect |
| 39. Q8×D251 | C23 | semidirect |
| 48. Dic1004 | C23 | semidirect |
| 49. #16860800 | C23 | semidirect |
| 50. #16860798 | C23 | semidirect |
| 51. #16860793 | C23 | semidirect |
| 60. SD16×C251 | C23 | semidirect |
| 91. C22×C251 | #137 | semidirect |
| 102. C2×C251 | C2×#137 | semidirect |
| 105. C251 | C22×#137 | semidirect |
| 113. C22×SD16 | D251 | semidirect |
| 132. C2×SD16 | C2×D251 | semidirect |
| 164. SD16 | C22×D251 | semidirect |
| 199. C22 | #22548744 | direct (N × H) |
| 209. C2 | C2×#22548744 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#16860809 | 2 |
| C22×Q8×D251 | 2 |
| C2×#22548744 | 2 |
| C22×Dic1004 | 2 |
| C22×#16860800 | 2 |
| C22×#16860798 | 2 |
| C22×#16860793 | 2 |
| C22×SD16×C251 | 2 |
| C22×#137 | 251 |