Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
424 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 424 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 |
|---|---|---|
| 2. #30632092 | C2 | semidirect |
| 3. #30632091 | C2 | semidirect |
| 4. #30632090 | C2 | semidirect |
| 7. #500×C251 | C2 | semidirect |
| 32. C8×D251 | Q8 | semidirect |
| 56. C251⋊C8 | C2×Q8 | semidirect |
| 62. C8×C251 | C2×Q8 | semidirect |
| 78. D251 | #500 | direct (N × H) |
| 79. C251 | C2×#500 | semidirect |
| 85. #500 | D251 | direct (N × H) |
| 142. C8 | Q8×D251 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4⋊Q8×D251 | 2 |
| #30632092 | 2 |
| #30632091 | 2 |
| #30632090 | 2 |
| #107×D251 | 2 |
| C4×C8×D251 | 2 |
| #500×C251 | 2 |
| C2×#500 | 251 |