Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
552 conjugacy classes of subgroups; only the 197 normal subgroups are shown.
This group has 552 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 |
|---|---|---|
| 3. #30632066 | C2 | direct (N × H) |
| 46. C2×C4×C251 | Q16 | semidirect |
| 56. C4×C251 | C2×Q16 | semidirect |
| 59. C2×C251 | #494 | semidirect |
| 62. C251 | C2×#494 | semidirect |
| 108. C2×C4 | #16860800 | semidirect |
| 120. C4 | C2×#16860800 | semidirect |
| 122. C2 | #30632066 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#16860800 | 2 |
| C2×#22548715 | 2 |
| #30632066 | 2 |
| C2×C4×C251⋊C8 | 2 |
| C2×C4⋊Q8×C251 | 2 |
| C2×#494 | 251 |