Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
360 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 101 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. #30631711 | C2 | semidirect |
| 3. C2×#22548643 | C2 | semidirect |
| 4. C43×C251 | C2 | semidirect |
| 7. #22548715 | C4 | semidirect |
| 8. #22548712 | C4 | semidirect |
| 9. #22548703 | C4 | semidirect |
| 36. C42×C251 | D4 | semidirect |
| 63. C4×C251 | #104 | semidirect |
| 72. C251 | #1962 | semidirect |
| 77. C43 | D251 | semidirect |
| 109. C42 | D1004 | semidirect |
| 137. C4 | #22548643 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #30632237 | 2 |
| #30631711 | 2 |
| C2×#22548643 | 2 |
| C43×C251 | 2 |
| #1962 | 251 |