Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
424 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 424 conjugacy classes of subgroups — too many to draw. Only its 141 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. #30632049 | C2 | semidirect |
| 3. #30632039 | C2 | semidirect |
| 4. #30632035 | C2 | semidirect |
| 5. #30631686 | C2 | semidirect |
| 6. C4×#16860794 | C2 | semidirect |
| 7. C2×C4⋊Q8×C251 | C2 | semidirect |
| 100. C251 | #3141 | semidirect |
| 103. C2×C4⋊Q8 | D251 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #30632237 | 2 |
| #30632049 | 2 |
| #30632039 | 2 |
| #30632035 | 2 |
| #30631686 | 2 |
| C4×#16860794 | 2 |
| C2×C4⋊Q8×C251 | 2 |
| #3141 | 251 |