Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
1048 conjugacy classes of subgroups; only the 197 normal subgroups are shown.
This group has 1048 conjugacy classes of subgroups — too many to draw. Only its 197 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×#16860795 | C2 | semidirect |
| 2. C2×#22548689 | C2 | semidirect |
| 3. #30631821 | C2 | direct (N × H) |
| 4. C2×#22548636 | C2 | semidirect |
| 5. C2×C22⋊(C251⋊C8) | C2 | semidirect |
| 6. C23×D4×C251 | C2 | semidirect |
| 7. C22×D1004 | C22 | semidirect |
| 10. C2×#16860795 | C22 | semidirect |
| 11. C22×C251⋊C8 | C22 | semidirect |
| 13. #22548689 | C22 | semidirect |
| 14. C2×C4⋊Dic251 | C22 | semidirect |
| 16. #22548636 | C22 | semidirect |
| 17. C22⋊(C251⋊C8) | C22 | semidirect |
| 23. C22×D4×C251 | C22 | semidirect |
| 28. C2×D1004 | C23 | semidirect |
| 34. C2×C251⋊C8 | C23 | semidirect |
| 36. C4⋊Dic251 | C23 | semidirect |
| 50. C2×D4×C251 | D4 | semidirect |
| 77. C23×C251 | D8 | semidirect |
| 83. D4×C251 | C2×D4 | semidirect |
| 101. C22×C251 | C2×D8 | semidirect |
| 114. C2×C251 | #447 | semidirect |
| 119. C251 | C2×#447 | semidirect |
| 121. C23×D4 | D251 | semidirect |
| 134. C22×D4 | C2×D251 | semidirect |
| 163. C2×D4 | C22⋊D251 | semidirect |
| 191. C23 | #16860795 | semidirect |
| 200. D4 | C2×C22⋊D251 | semidirect |
| 225. C22 | C2×#16860795 | semidirect |
| 235. C2 | #30631821 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#16860795 | 2 |
| C2×#22548689 | 2 |
| #30631821 | 2 |
| C2×#22548636 | 2 |
| C2×C22⋊(C251⋊C8) | 2 |
| C23×D4×C251 | 2 |
| C2×#447 | 251 |