Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
848 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 848 conjugacy classes of subgroups — too many to draw. Only its 125 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×#22548637 | C2 | semidirect |
| 3. C2×#22548636 | C2 | semidirect |
| 4. C2×#22548635 | C2 | semidirect |
| 5. C2×(C2×D251)⋊C8 | C2 | semidirect |
| 6. #30631544 | C2 | semidirect |
| 7. C2×#102×C251 | C2 | semidirect |
| 16. C2×D4×D251 | C4 | semidirect |
| 18. C22×C251⋊C8 | C22 | semidirect |
| 19. C2×C4⋊Dic251 | C22 | semidirect |
| 27. C22×C8×C251 | C22 | semidirect |
| 28. C2×C4⋊C4×C251 | C22 | semidirect |
| 104. D1004 | C22⋊C4 | semidirect |
| 128. D4×C251 | C22⋊C4 | semidirect |
| 167. C2×D251 | #102 | semidirect |
| 185. C251 | #1786 | semidirect |
| 191. C2×#102 | D251 | semidirect |
| 206. C22×C8 | C2×D251 | semidirect |
| 208. C2×C4⋊C4 | C2×D251 | semidirect |
| 303. D4 | (C2×D251)⋊C4 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D4×D251 | 2 |
| C2×#22548637 | 2 |
| C2×#22548636 | 2 |
| C2×#22548635 | 2 |
| C2×(C2×D251)⋊C8 | 2 |
| #30631544 | 2 |
| C2×#102×C251 | 2 |
| #1786 | 251 |