Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
492 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 127 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. #30632235 | C2 | semidirect |
| 2. C4×D4×D251 | C2 | semidirect |
| 3. #30631999 | C2 | semidirect |
| 4. #30631968 | C2 | semidirect |
| 5. #30631967 | C2 | semidirect |
| 6. #30631879 | C2 | semidirect |
| 7. #30631819 | C2 | semidirect |
| 8. D8×Dic251 | C2 | semidirect |
| 9. #30631767 | C2 | semidirect |
| 10. #30631739 | C2 | semidirect |
| 11. #459×C251 | C2 | semidirect |
| 16. #22548715 | C22 | semidirect |
| 23. D4×Dic251 | C22 | semidirect |
| 30. #22548649 | C22 | semidirect |
| 31. #22548648 | C22 | semidirect |
| 32. C4⋊(C251⋊C8) | C22 | semidirect |
| 35. #22548636 | C22 | semidirect |
| 37. C8×Dic251 | C22 | semidirect |
| 39. #127×C251 | C22 | semidirect |
| 41. C4⋊C8×C251 | C22 | semidirect |
| 42. #102×C251 | C22 | semidirect |
| 91. D1004 | #41 | semidirect |
| 107. C4×D251 | D8 | semidirect |
| 116. D4×C251 | #41 | semidirect |
| 154. C251 | #3100 | semidirect |
| 162. #459 | D251 | semidirect |
| 173. #127 | C2×D251 | semidirect |
| 191. C4⋊C8 | C2×D251 | semidirect |
| 195. #102 | C2×D251 | semidirect |
| 256. D4 | #16860809 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #30632235 | 2 |
| C4×D4×D251 | 2 |
| #30631999 | 2 |
| #30631968 | 2 |
| #30631967 | 2 |
| #30631879 | 2 |
| #30631819 | 2 |
| D8×Dic251 | 2 |
| #30631767 | 2 |
| #30631739 | 2 |
| #459×C251 | 2 |
| #3100 | 251 |