Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
376 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 376 conjugacy classes of subgroups — too many to draw. Only its 105 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×#22548635 | C2 | semidirect |
| 3. C2×#22548625 | C2 | semidirect |
| 4. #30631588 | C2 | semidirect |
| 5. C2×#106×C251 | C2 | semidirect |
| 9. C2×D2008 | C4 | semidirect |
| 61. C8×C251 | C22⋊C4 | semidirect |
| 82. C251 | #1972 | semidirect |
| 85. C2×#106 | D251 | semidirect |
| 144. C8 | (C2×D251)⋊C4 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D2008 | 2 |
| C2×#22548635 | 2 |
| C2×#22548625 | 2 |
| #30631588 | 2 |
| C2×#106×C251 | 2 |
| #1972 | 251 |