Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
140 conjugacy classes of subgroups; only the 47 normal subgroups are shown.
This group has 140 conjugacy classes of subgroups — too many to draw. Only its 47 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 |
|---|---|---|
| 3. #30631515 | C2 | semidirect |
| 4. #30631514 | C2 | semidirect |
| 5. #30631491 | C2 | semidirect |
| 7. #358×C251 | C2 | semidirect |
| 66. C251 | #2235 | semidirect |
| 73. #358 | D251 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #30631925 | 2 |
| #107×D251 | 2 |
| #30631515 | 2 |
| #30631514 | 2 |
| #30631491 | 2 |
| (C2×D251)⋊C16 | 2 |
| #358×C251 | 2 |
| #2235 | 251 |