Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
464 conjugacy classes of subgroups; only the 189 normal subgroups are shown.
This group has 464 conjugacy classes of subgroups — too many to draw. Only its 189 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×#22548721 | C2 | semidirect |
| 3. #30631810 | C2 | direct (N × H) |
| 4. C2×#22548651 | C2 | semidirect |
| 5. C2×#22548643 | C2 | semidirect |
| 6. C2×#97×C251 | C2 | semidirect |
| 8. #22548737 | C4 | semidirect |
| 10. C2×Dic1004 | C4 | semidirect |
| 11. C2×#16860799 | C4 | semidirect |
| 12. C2×D2008 | C4 | semidirect |
| 14. #22548721 | C22 | semidirect |
| 18. #22548651 | C22 | semidirect |
| 19. #22548643 | C22 | semidirect |
| 23. #97×C251 | C22 | semidirect |
| 32. Dic1004 | C2×C4 | semidirect |
| 33. #16860799 | C2×C4 | semidirect |
| 34. D2008 | C2×C4 | semidirect |
| 88. C2×C251 | #444 | semidirect |
| 91. C251 | C2×#444 | semidirect |
| 98. C2×#97 | D251 | semidirect |
| 115. #97 | C2×D251 | semidirect |
| 181. C2 | #30631810 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22548737 | 2 |
| C2×#22548721 | 2 |
| #30631810 | 2 |
| C2×#22548651 | 2 |
| C2×#22548643 | 2 |
| C2×#97×C251 | 2 |
| C2×#444 | 251 |