Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
488 conjugacy classes of subgroups; only the 221 normal subgroups are shown.
This group has 488 conjugacy classes of subgroups — too many to draw. Only its 221 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. C4×#16860800 | C2 | direct (N × H) |
| 10. C2×#16860800 | C4 | direct (N × H) |
| 36. #16860800 | C2×C4 | direct (N × H) |
| 78. C2×C4×C251 | Q16 | semidirect |
| 93. C4×C251 | C2×Q16 | semidirect |
| 98. C2×C251 | C4×Q16 | semidirect |
| 102. C251 | C2×C4×Q16 | semidirect |
| 179. C2×C4 | #16860800 | direct (N × H) |
| 198. C4 | C2×#16860800 | direct (N × H) |
| 201. C2 | C4×#16860800 | 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×C4×Dic502 | 2 |
| C4×#16860800 | 2 |
| C2×#22548648 | 2 |
| C2×#22548639 | 2 |
| C2×#22548638 | 2 |
| C2×C4×C251⋊C8 | 2 |
| C2×C4×Q8×C251 | 2 |
| C2×C4×Q16 | 251 |