Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
812 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 812 conjugacy classes of subgroups — too many to draw. Only its 165 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×#16860811 | C2 | semidirect |
| 2. C22×#16860797 | C2 | semidirect |
| 3. C22×D2008 | C2 | semidirect |
| 4. C2×#22548690 | C2 | semidirect |
| 5. #30631835 | C2 | direct (N × H) |
| 6. C2×#22548635 | C2 | semidirect |
| 7. C2×(C2×D251)⋊C8 | C2 | semidirect |
| 8. C2×#103×C251 | C2 | semidirect |
| 12. C2×#16860811 | C22 | semidirect |
| 20. C2×#16860797 | C22 | semidirect |
| 22. C2×D2008 | C22 | semidirect |
| 25. #22548690 | C22 | semidirect |
| 27. #22548635 | C22 | semidirect |
| 28. (C2×D251)⋊C8 | C22 | semidirect |
| 32. #103×C251 | C22 | semidirect |
| 48. C2×D1004 | D4 | semidirect |
| 65. C2×Q8×C251 | D4 | semidirect |
| 93. D1004 | C2×D4 | semidirect |
| 104. Q8×C251 | C2×D4 | semidirect |
| 136. C2×C251 | #449 | semidirect |
| 143. C251 | C2×#449 | semidirect |
| 150. C2×#103 | D251 | semidirect |
| 174. #103 | C2×D251 | semidirect |
| 185. C2×Q8 | D1004 | semidirect |
| 233. Q8 | C2×D1004 | semidirect |
| 283. C2 | #30631835 | 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×#16860797 | 2 |
| C22×D2008 | 2 |
| C2×#22548690 | 2 |
| #30631835 | 2 |
| C2×#22548635 | 2 |
| C2×(C2×D251)⋊C8 | 2 |
| C2×#103×C251 | 2 |
| C2×#449 | 251 |