Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
156 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 156 conjugacy classes of subgroups — too many to draw. Only its 69 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 |
|---|---|---|
| 4. #30631514 | C2 | semidirect |
| 5. #30631513 | C2 | semidirect |
| 6. #30631512 | C2 | semidirect |
| 7. #367×C251 | C2 | semidirect |
| 11. #22548654 | C4 | semidirect |
| 30. C251⋊C16 | C2×C4 | semidirect |
| 34. C16×C251 | C2×C4 | semidirect |
| 63. C251 | #2159 | semidirect |
| 69. #367 | D251 | semidirect |
| 98. C16 | C4×D251 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22548654 | 2 |
| #30631724 | 2 |
| #107×D251 | 2 |
| #30631514 | 2 |
| #30631513 | 2 |
| #30631512 | 2 |
| #367×C251 | 2 |
| #2159 | 251 |