Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
220 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 220 conjugacy classes of subgroups — too many to draw. Only its 51 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. C2×#22548658 | C2 | semidirect |
| 3. #30631925 | C2 | semidirect |
| 4. #30631491 | C2 | semidirect |
| 5. #30631489 | C2 | semidirect |
| 6. (C2×D251)⋊C16 | C2 | semidirect |
| 7. C2×Q32×C251 | C2 | semidirect |
| 85. C251 | #2189 | semidirect |
| 88. C2×Q32 | D251 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22548738 | 2 |
| C2×#22548658 | 2 |
| #30631925 | 2 |
| #30631491 | 2 |
| #30631489 | 2 |
| (C2×D251)⋊C16 | 2 |
| C2×Q32×C251 | 2 |
| #2189 | 251 |