Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
412 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 412 conjugacy classes of subgroups — too many to draw. Only its 145 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. #30632083 | C2 | semidirect |
| 3. #30632061 | C2 | semidirect |
| 4. #30632037 | C2 | semidirect |
| 5. #30632035 | C2 | semidirect |
| 6. #30631918 | C2 | semidirect |
| 7. C4×#16860797 | C2 | semidirect |
| 8. C2×C4×C251⋊C8 | C2 | semidirect |
| 9. #533×C251 | C2 | semidirect |
| 76. C251⋊C8 | #41 | semidirect |
| 84. C2×C4×C251 | SD16 | semidirect |
| 112. C251 | #3167 | semidirect |
| 114. #533 | D251 | semidirect |
| 195. C2×C4 | #16860797 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #30632237 | 2 |
| #30632083 | 2 |
| #30632061 | 2 |
| #30632037 | 2 |
| #30632035 | 2 |
| #30631918 | 2 |
| C4×#16860797 | 2 |
| C2×C4×C251⋊C8 | 2 |
| #533×C251 | 2 |
| #3167 | 251 |