Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
484 conjugacy classes of subgroups; only the 297 normal subgroups are shown.
This group has 484 conjugacy classes of subgroups — too many to draw. Only its 297 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. #30631714 | C2 | semidirect |
| 3. #30631711 | C2 | semidirect |
| 4. C2×C4⋊(C251⋊C8) | C2 | semidirect |
| 61. C4×C251 | #131 | semidirect |
| 68. C251 | #2906 | semidirect |
| 130. C4 | #22548722 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22548722 | 2 |
| #30631714 | 2 |
| #30631711 | 2 |
| C2×C4⋊(C251⋊C8) | 2 |
| C4×#41×C251 | 2 |
| #2906 | 251 |