Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
316 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 316 conjugacy classes of subgroups — too many to draw. Only its 105 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×#22548648 | C2 | semidirect |
| 3. C2×#22548646 | C2 | semidirect |
| 5. #30631449 | C2 | semidirect |
| 6. #30631449 | C2 | semidirect |
| 18. C22⋊(C251⋊C8) | C4 | semidirect |
| 120. C251 | #1854 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22548674 | 2 |
| C2×#22548648 | 2 |
| C2×#22548646 | 2 |
| C2×C22⋊(C251⋊C8) | 2 |
| #30631449 | 2 |
| #380×C251 | 2 |
| #1854 | 251 |