Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
388 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 388 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. #30632020 | C2 | semidirect |
| 4. #30631982 | C2 | semidirect |
| 5. #30631926 | C2 | semidirect |
| 6. #30631894 | C2 | semidirect |
| 7. #30631843 | C2 | semidirect |
| 8. C4×#16860800 | C2 | semidirect |
| 10. C2×#22548639 | C2 | semidirect |
| 92. D4×C251 | Q16 | semidirect |
| 122. C251 | #3299 | semidirect |
| 208. D4 | #16860800 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #30632394 | 2 |
| #30632037 | 2 |
| #30632020 | 2 |
| #30631982 | 2 |
| #30631926 | 2 |
| #30631894 | 2 |
| #30631843 | 2 |
| C4×#16860800 | 2 |
| D4×C251⋊C8 | 2 |
| C2×#22548639 | 2 |
| D4×Q8×C251 | 2 |
| #3299 | 251 |