Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
620 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 620 conjugacy classes of subgroups — too many to draw. Only its 101 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×#22548643 | C2 | semidirect |
| 3. #30631686 | C2 | semidirect |
| 4. C2×#22548632 | C2 | semidirect |
| 5. #390×C251 | C2 | semidirect |
| 8. #22548760 | C4 | semidirect |
| 13. C2×#16860794 | C22 | semidirect |
| 19. C2×C4⋊C4×C251 | C22 | semidirect |
| 21. C2×C42×C251 | C22 | semidirect |
| 58. Dic502 | C22⋊C4 | semidirect |
| 60. D1004 | C22⋊C4 | semidirect |
| 112. C251 | #1792 | semidirect |
| 118. #390 | D251 | semidirect |
| 128. C2×C4⋊C4 | C2×D251 | semidirect |
| 130. C2×C42 | C2×D251 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22548760 | 2 |
| C2×#22548643 | 2 |
| #30631686 | 2 |
| C2×#22548632 | 2 |
| #390×C251 | 2 |
| #1792 | 251 |