Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
150 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 150 conjugacy classes of subgroups — too many to draw. Only its 53 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. #30631514 | C2 | semidirect |
| 3. #30631487 | C2 | semidirect |
| 4. C22⋊(C251⋊C16) | C2 | semidirect |
| 5. C2×#107×C251 | C2 | semidirect |
| 59. C251 | #2233 | semidirect |
| 62. C2×#107 | D251 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #30631923 | 2 |
| #30631514 | 2 |
| #30631487 | 2 |
| C22⋊(C251⋊C16) | 2 |
| C2×#107×C251 | 2 |
| #2233 | 251 |