Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
616 conjugacy classes of subgroups; only the 205 normal subgroups are shown.
This group has 616 conjugacy classes of subgroups — too many to draw. Only its 205 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. C2×D4×Dic251 | C2 | semidirect |
| 3. C2×#22548677 | C2 | semidirect |
| 4. #30631767 | C2 | direct (N × H) |
| 5. C2×#22548648 | C2 | semidirect |
| 6. C2×#22548637 | C2 | semidirect |
| 7. C2×C8×Dic251 | C2 | semidirect |
| 8. C2×#102×C251 | C2 | semidirect |
| 12. C2×#16860795 | C4 | semidirect |
| 16. D4×Dic251 | C22 | semidirect |
| 18. #22548677 | C22 | semidirect |
| 23. #22548648 | C22 | semidirect |
| 24. #22548637 | C22 | semidirect |
| 25. C8×Dic251 | C22 | semidirect |
| 29. #102×C251 | C22 | semidirect |
| 33. C2×D1004 | C2×C4 | semidirect |
| 42. #16860795 | C2×C4 | semidirect |
| 43. C2×C251⋊C8 | C2×C4 | semidirect |
| 54. C2×D4×C251 | C2×C4 | semidirect |
| 68. D1004 | C22×C4 | semidirect |
| 73. C2×Dic251 | D8 | semidirect |
| 77. C251⋊C8 | C22×C4 | semidirect |
| 85. D4×C251 | C22×C4 | semidirect |
| 111. Dic251 | C2×D8 | semidirect |
| 113. C2×C251 | C4×D8 | semidirect |
| 118. C251 | C2×C4×D8 | semidirect |
| 126. C2×#102 | D251 | semidirect |
| 147. #102 | C2×D251 | semidirect |
| 157. C2×D4 | C4×D251 | semidirect |
| 195. D4 | C2×C4×D251 | semidirect |
| 233. C2 | #30631767 | 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×D4×Dic251 | 2 |
| C2×#22548677 | 2 |
| #30631767 | 2 |
| C2×#22548648 | 2 |
| C2×#22548637 | 2 |
| C2×C8×Dic251 | 2 |
| C2×#102×C251 | 2 |
| C2×C4×D8 | 251 |