Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
472 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 472 conjugacy classes of subgroups — too many to draw. Only its 149 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. C22×#16860800 | C2 | semidirect |
| 3. #30632066 | C2 | semidirect |
| 4. #30631926 | C2 | semidirect |
| 5. #30631897 | C2 | semidirect |
| 6. #30631894 | C2 | semidirect |
| 7. #30631843 | C2 | semidirect |
| 8. #30631842 | C2 | semidirect |
| 9. C4×#16860800 | C2 | semidirect |
| 52. #16860800 | D4 | direct (N × H) |
| 100. D4×C251 | Q16 | semidirect |
| 113. C22×C251 | C2×Q16 | semidirect |
| 120. C4×C251 | C2×Q16 | semidirect |
| 130. C251 | D4×Q16 | semidirect |
| 224. D4 | #16860800 | direct (N × H) |
| 244. C22 | C2×#16860800 | semidirect |
| 254. C4 | C2×#16860800 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#16860800 | 2 |
| D4×Dic502 | 2 |
| #30632066 | 2 |
| #30631926 | 2 |
| #30631897 | 2 |
| #30631894 | 2 |
| #30631843 | 2 |
| #30631842 | 2 |
| C4×#16860800 | 2 |
| D4×C251⋊C8 | 2 |
| D4×Q8×C251 | 2 |
| D4×Q16 | 251 |