Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
544 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 544 conjugacy classes of subgroups — too many to draw. Only its 165 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×#22548713 | C2 | semidirect |
| 4. #30631890 | C2 | direct (N × H) |
| 5. C2×Dic251⋊C8 | C2 | semidirect |
| 6. C2×#22548640 | C2 | semidirect |
| 7. C2×#22548639 | C2 | semidirect |
| 15. #22548713 | C22 | semidirect |
| 23. Dic251⋊C8 | C22 | semidirect |
| 24. #22548640 | C22 | semidirect |
| 25. #22548639 | C22 | semidirect |
| 74. C2×Dic251 | SD16 | semidirect |
| 111. Dic251 | C2×SD16 | semidirect |
| 113. C2×C251 | #461 | semidirect |
| 117. C251 | C2×#461 | semidirect |
| 231. C2 | #30631890 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#16860798 | 2 |
| C2×#22548713 | 2 |
| C2×D4×Dic251 | 2 |
| #30631890 | 2 |
| C2×Dic251⋊C8 | 2 |
| C2×#22548640 | 2 |
| C2×#22548639 | 2 |
| C22×SD16×C251 | 2 |
| C2×#461 | 251 |