Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
548 conjugacy classes of subgroups; only the 135 normal subgroups are shown.
This group has 548 conjugacy classes of subgroups — too many to draw. Only its 135 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 |
|---|---|---|
| 1. C2×#22548743 | C2 | semidirect |
| 2. C2×#22548740 | C2 | semidirect |
| 3. #30632233 | C2 | semidirect |
| 4. C2×#22548677 | C2 | semidirect |
| 5. #30631905 | C2 | semidirect |
| 6. #30631901 | C2 | semidirect |
| 7. #30631891 | C2 | semidirect |
| 8. #30631881 | C2 | semidirect |
| 9. #30631710 | C2 | semidirect |
| 10. #30631686 | C2 | semidirect |
| 11. #417×C251 | C2 | semidirect |
| 22. #22548713 | C22 | semidirect |
| 23. #22548711 | C22 | semidirect |
| 24. #22548704 | C22 | semidirect |
| 25. #22548702 | C22 | semidirect |
| 36. Dic251⋊C8 | C22 | semidirect |
| 37. Dic251⋊C8 | C22 | semidirect |
| 38. #22548638 | C22 | semidirect |
| 39. #22548635 | C22 | semidirect |
| 43. #103×C251 | C22 | semidirect |
| 44. #102×C251 | C22 | semidirect |
| 51. C2×D1004 | D4 | semidirect |
| 158. Dic251 | AGL(1,ℤ/8) | semidirect |
| 166. C251 | #3036 | semidirect |
| 178. #417 | D251 | semidirect |
| 209. #103 | C2×D251 | semidirect |
| 211. #102 | C2×D251 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22548743 | 2 |
| C2×#22548740 | 2 |
| #30632233 | 2 |
| C2×#22548677 | 2 |
| #30631905 | 2 |
| #30631901 | 2 |
| #30631891 | 2 |
| #30631881 | 2 |
| #30631710 | 2 |
| #30631686 | 2 |
| #417×C251 | 2 |
| #3036 | 251 |