Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
616 conjugacy classes of subgroups; only the 253 normal subgroups are shown.
This group has 616 conjugacy classes of subgroups — too many to draw. Only its 253 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×C8×D251 | C2 | semidirect |
| 3. #30631752 | C2 | direct (N × H) |
| 4. C2×(C2×D251)⋊C8 | C2 | semidirect |
| 5. C2×C4×C251⋊C8 | C2 | semidirect |
| 6. C2×C4⋊C8×C251 | C2 | semidirect |
| 12. C2×C8×D251 | C22 | semidirect |
| 17. (C2×D251)⋊C8 | C22 | semidirect |
| 18. C4×C251⋊C8 | C22 | semidirect |
| 21. C4⋊C8×C251 | C22 | semidirect |
| 23. C2×D1004 | C8 | semidirect |
| 31. C2×C251⋊C8 | D4 | semidirect |
| 46. C22×D251 | C2×C8 | semidirect |
| 48. D1004 | C2×C8 | semidirect |
| 55. C251⋊C8 | C2×D4 | semidirect |
| 58. C2×C4×C251 | C2×C8 | semidirect |
| 73. C2×D251 | C22×C8 | semidirect |
| 76. C4×C251 | C22×C8 | semidirect |
| 80. C2×C251 | C8×D4 | semidirect |
| 85. C251 | C2×C8×D4 | semidirect |
| 90. C2×C4⋊C8 | D251 | semidirect |
| 105. C4⋊C8 | C2×D251 | semidirect |
| 142. C2×C4 | C8×D251 | semidirect |
| 163. C4 | C2×C8×D251 | semidirect |
| 167. C2 | #30631752 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C8×D251 | 2 |
| C2×C4×D1004 | 2 |
| #30631752 | 2 |
| C2×(C2×D251)⋊C8 | 2 |
| C2×C4×C251⋊C8 | 2 |
| C2×C4⋊C8×C251 | 2 |
| C2×C8×D4 | 251 |