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×#22548747 | C2 | direct (N × H) |
| 4. C22×#16860800 | C2 | semidirect |
| 5. C22×#16860799 | C2 | semidirect |
| 6. C22×#16860797 | C2 | semidirect |
| 7. C22×#16860793 | C2 | semidirect |
| 8. C22×Q16×C251 | C2 | semidirect |
| 14. C2×Q8×D251 | C22 | semidirect |
| 20. #22548747 | C22 | direct (N × H) |
| 21. C2×#16860800 | C22 | semidirect |
| 22. C2×#16860799 | C22 | semidirect |
| 23. C2×#16860797 | C22 | semidirect |
| 24. C2×#16860793 | C22 | semidirect |
| 28. C2×Q16×C251 | C22 | semidirect |
| 38. Q8×D251 | C23 | semidirect |
| 48. #16860800 | C23 | semidirect |
| 49. #16860799 | C23 | semidirect |
| 50. #16860797 | C23 | semidirect |
| 51. #16860793 | C23 | semidirect |
| 60. Q16×C251 | C23 | semidirect |
| 89. C22×C251 | #137 | semidirect |
| 101. C2×C251 | C2×#137 | semidirect |
| 105. C251 | C22×#137 | semidirect |
| 111. C22×Q16 | D251 | semidirect |
| 130. C2×Q16 | C2×D251 | semidirect |
| 162. Q16 | C22×D251 | semidirect |
| 199. C22 | #22548747 | direct (N × H) |
| 209. C2 | C2×#22548747 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#16860811 | 2 |
| C22×Q8×D251 | 2 |
| C2×#22548747 | 2 |
| C22×#16860800 | 2 |
| C22×#16860799 | 2 |
| C22×#16860797 | 2 |
| C22×#16860793 | 2 |
| C22×Q16×C251 | 2 |
| C22×#137 | 251 |