Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
150 conjugacy classes of subgroups; only the 47 normal subgroups are shown.
This group has 150 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 |
|---|---|---|
| 2. #107×D251 | C2 | semidirect |
| 3. #30631514 | C2 | semidirect |
| 4. #30631489 | C2 | semidirect |
| 5. #30631487 | C2 | semidirect |
| 6. (C2×D251)⋊C16 | C2 | semidirect |
| 7. #367×C251 | C2 | semidirect |
| 70. C251 | #2233 | semidirect |
| 75. #367 | D251 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #30631924 | 2 |
| #107×D251 | 2 |
| #30631514 | 2 |
| #30631489 | 2 |
| #30631487 | 2 |
| (C2×D251)⋊C16 | 2 |
| #367×C251 | 2 |
| #2233 | 251 |