Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
420 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 420 conjugacy classes of subgroups — too many to draw. Only its 141 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. #30632037 | C2 | semidirect |
| 3. #30632015 | C2 | semidirect |
| 4. #30631972 | C2 | semidirect |
| 5. #30631918 | C2 | semidirect |
| 6. #30631889 | C2 | semidirect |
| 7. #30631826 | C2 | semidirect |
| 8. C4×#16860797 | C2 | semidirect |
| 9. D4×C251⋊C8 | C2 | semidirect |
| 10. C2×#22548639 | C2 | semidirect |
| 11. D4×Q8×C251 | C2 | semidirect |
| 94. Q8×C251 | #41 | semidirect |
| 95. D4×C251 | SD16 | semidirect |
| 128. C251 | #3298 | semidirect |
| 130. D4×Q8 | D251 | semidirect |
| 213. Q8 | #16860809 | semidirect |
| 217. D4 | #16860797 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #30632341 | 2 |
| #30632037 | 2 |
| #30632015 | 2 |
| #30631972 | 2 |
| #30631918 | 2 |
| #30631889 | 2 |
| #30631826 | 2 |
| C4×#16860797 | 2 |
| D4×C251⋊C8 | 2 |
| C2×#22548639 | 2 |
| D4×Q8×C251 | 2 |
| #3298 | 251 |