Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
618 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 618 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×#22548643 | C2 | semidirect |
| 3. #30631651 | C2 | semidirect |
| 4. C4×C22⋊C4×C251 | C2 | semidirect |
| 8. C2×#16860810 | C4 | semidirect |
| 10. C22×Dic502 | C4 | semidirect |
| 11. C22×D1004 | C4 | semidirect |
| 14. C2×#16860794 | C22 | semidirect |
| 20. C2×C42×C251 | C22 | semidirect |
| 61. Dic502 | C22⋊C4 | semidirect |
| 64. D1004 | C22⋊C4 | semidirect |
| 99. C22×C251 | #104 | semidirect |
| 119. C251 | #1789 | semidirect |
| 124. C4×C22⋊C4 | D251 | semidirect |
| 137. C2×C42 | C2×D251 | semidirect |
| 223. C22 | #22548643 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#16860810 | 2 |
| C2×#22548643 | 2 |
| #30631651 | 2 |
| C4×C22⋊C4×C251 | 2 |
| #1789 | 251 |