Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
612 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 612 conjugacy classes of subgroups — too many to draw. Only its 117 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×#22548640 | C2 | semidirect |
| 3. C2×#22548637 | C2 | semidirect |
| 4. #30631547 | C2 | semidirect |
| 5. C2×C22⋊C8×C251 | C2 | semidirect |
| 9. C2×#16860810 | C4 | semidirect |
| 60. Dic502 | C22⋊C4 | semidirect |
| 63. D1004 | C22⋊C4 | semidirect |
| 115. C251 | #1788 | semidirect |
| 120. C2×C22⋊C8 | D251 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#16860810 | 2 |
| C2×#22548640 | 2 |
| C2×#22548637 | 2 |
| #30631547 | 2 |
| C2×C22⋊C8×C251 | 2 |
| #1788 | 251 |