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×#16860810 | C2 | semidirect |
| 2. C22×#16860798 | C2 | semidirect |
| 3. C22×#16860795 | C2 | semidirect |
| 4. #30631830 | C2 | direct (N × H) |
| 5. C2×#22548638 | C2 | semidirect |
| 6. C2×#22548635 | C2 | semidirect |
| 7. C2×C22⋊(C251⋊C8) | C2 | semidirect |
| 8. C2×#121×C251 | C2 | semidirect |
| 12. C2×#16860810 | C22 | semidirect |
| 18. C2×#16860798 | C22 | semidirect |
| 20. C2×#16860795 | C22 | semidirect |
| 23. #22548638 | C22 | semidirect |
| 24. #22548635 | C22 | semidirect |
| 25. C22⋊(C251⋊C8) | C22 | semidirect |
| 30. #121×C251 | C22 | semidirect |
| 39. C2×Dic502 | D4 | semidirect |
| 43. C2×D1004 | D4 | semidirect |
| 80. Dic502 | C2×D4 | semidirect |
| 83. D1004 | C2×D4 | semidirect |
| 138. C2×C251 | #449 | semidirect |
| 143. C251 | C2×#449 | semidirect |
| 148. C2×#121 | D251 | semidirect |
| 171. #121 | C2×D251 | semidirect |
| 283. C2 | #30631830 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#16860810 | 2 |
| C22×#16860798 | 2 |
| C22×#16860795 | 2 |
| #30631830 | 2 |
| C2×#22548638 | 2 |
| C2×#22548635 | 2 |
| C2×C22⋊(C251⋊C8) | 2 |
| C2×#121×C251 | 2 |
| C2×#449 | 251 |