Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
456 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 107 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×C4⋊C4×D251 | C2 | semidirect |
| 3. C2×#22548636 | C2 | semidirect |
| 4. C2×(C2×D251)⋊C8 | C2 | semidirect |
| 5. #30631450 | C2 | semidirect |
| 6. #30631449 | C2 | semidirect |
| 7. C2×#102×C251 | C2 | semidirect |
| 13. #22548686 | C4 | semidirect |
| 47. C4⋊Dic251 | C2×C4 | semidirect |
| 48. C4⋊Dic251 | D4 | semidirect |
| 57. C2×D4×C251 | C2×C4 | semidirect |
| 64. C4⋊C4×C251 | D4 | semidirect |
| 130. C2×D251 | #102 | semidirect |
| 148. C251 | #1874 | semidirect |
| 153. C2×#102 | D251 | semidirect |
| 185. C2×D4 | C4×D251 | semidirect |
| 212. C4⋊C4 | C22⋊D251 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22548686 | 2 |
| C2×C4⋊C4×D251 | 2 |
| C2×#22548636 | 2 |
| C2×(C2×D251)⋊C8 | 2 |
| #30631450 | 2 |
| #30631449 | 2 |
| C2×#102×C251 | 2 |
| #1874 | 251 |