Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
872 conjugacy classes of subgroups; only the 237 normal subgroups are shown.
This group has 872 conjugacy classes of subgroups — too many to draw. Only its 237 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×C4×Dic502 | C2 | semidirect |
| 3. #30631589 | C2 | semidirect |
| 4. #30631587 | C2 | semidirect |
| 5. #30631547 | C2 | semidirect |
| 6. #30631546 | C2 | semidirect |
| 7. #30631534 | C2 | semidirect |
| 8. C4×C22⋊C4×C251 | C2 | semidirect |
| 10. C2×#16860810 | C4 | semidirect |
| 60. Dic502 | C22⋊C4 | semidirect |
| 85. C2×C4×C251 | #41 | semidirect |
| 114. C251 | #2341 | semidirect |
| 123. C4×C22⋊C4 | D251 | semidirect |
| 200. C2×C4 | #16860810 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#16860810 | 2 |
| C2×C4×Dic502 | 2 |
| #30631589 | 2 |
| #30631587 | 2 |
| #30631547 | 2 |
| #30631546 | 2 |
| #30631534 | 2 |
| C4×C22⋊C4×C251 | 2 |
| #2341 | 251 |