Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
346 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 346 conjugacy classes of subgroups — too many to draw. Only its 79 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. #30632161 | C2 | semidirect |
| 3. #30631704 | C2 | semidirect |
| 4. #30631691 | C2 | semidirect |
| 5. #30631457 | C2 | semidirect |
| 6. #30631443 | C2 | semidirect |
| 7. #410×C251 | C2 | semidirect |
| 11. C2×#16860797 | C4 | semidirect |
| 12. C2×#16860795 | C4 | semidirect |
| 40. C2×C251⋊C8 | C2×C4 | semidirect |
| 49. C2×Q8×C251 | C2×C4 | semidirect |
| 51. C2×D4×C251 | C2×C4 | semidirect |
| 115. C251 | #1904 | semidirect |
| 121. #410 | D251 | semidirect |
| 146. C2×Q8 | C4×D251 | semidirect |
| 154. C2×D4 | C4×D251 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22548740 | 2 |
| #30632161 | 2 |
| #30631704 | 2 |
| #30631691 | 2 |
| #30631457 | 2 |
| #30631443 | 2 |
| #410×C251 | 2 |
| #1904 | 251 |