Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
448 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 448 conjugacy classes of subgroups — too many to draw. Only its 141 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. C22×#16860800 | C2 | semidirect |
| 4. #30631960 | C2 | direct (N × H) |
| 5. C2×#22548650 | C2 | semidirect |
| 6. C2×#22548634 | C2 | semidirect |
| 7. C2×#22548633 | C2 | semidirect |
| 16. C2×#16860800 | C22 | semidirect |
| 25. #22548650 | C22 | semidirect |
| 26. #22548634 | C22 | semidirect |
| 27. #22548633 | C22 | semidirect |
| 131. C2×C251 | #473 | semidirect |
| 133. C251 | C2×#473 | semidirect |
| 265. C2 | #30631960 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22548745 | 2 |
| C22×#16860800 | 2 |
| C2×#22548722 | 2 |
| #30631960 | 2 |
| C2×#22548650 | 2 |
| C2×#22548634 | 2 |
| C2×#22548633 | 2 |
| C2×#137×C251 | 2 |
| C2×#473 | 251 |