Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
1102 conjugacy classes of subgroups; only the 213 normal subgroups are shown.
This group has 1102 conjugacy classes of subgroups — too many to draw. Only its 213 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 |
|---|---|---|
| 1. C2×#22548698 | C2 | semidirect |
| 3. #30631566 | C2 | semidirect |
| 4. #30631560 | C2 | semidirect |
| 5. #30631550 | C2 | semidirect |
| 6. #30631543 | C2 | semidirect |
| 7. C24×C4×C251 | C2 | semidirect |
| 12. C2×Dic251⋊C4 | C22 | semidirect |
| 17. C2×(C2×D251)⋊C4 | C22 | semidirect |
| 18. C251⋊#95 | C22 | semidirect |
| 48. C22×C4×C251 | D4 | semidirect |
| 84. C22×C251 | #123 | semidirect |
| 101. C251 | #2849 | semidirect |
| 103. C24×C4 | D251 | semidirect |
| 144. C22×C4 | C22⋊D251 | semidirect |
| 189. C22 | #22548698 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22548698 | 2 |
| C2×#22548684 | 2 |
| #30631566 | 2 |
| #30631560 | 2 |
| #30631550 | 2 |
| #30631543 | 2 |
| C24×C4×C251 | 2 |
| #2849 | 251 |