Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
540 conjugacy classes of subgroups; only the 189 normal subgroups are shown.
This group has 540 conjugacy classes of subgroups — too many to draw. Only its 189 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. #30631583 | C2 | semidirect |
| 4. #30631578 | C2 | semidirect |
| 5. #30631549 | C2 | semidirect |
| 6. #30631546 | C2 | semidirect |
| 7. #30631533 | C2 | semidirect |
| 8. C4×C4⋊C4×C251 | C2 | semidirect |
| 11. C4×D1004 | C4 | semidirect |
| 96. C251 | #2319 | semidirect |
| 104. C4×C4⋊C4 | D251 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×D1004 | 2 |
| #30631588 | 2 |
| #30631583 | 2 |
| #30631578 | 2 |
| #30631549 | 2 |
| #30631546 | 2 |
| #30631533 | 2 |
| C4×C4⋊C4×C251 | 2 |
| #2319 | 251 |