Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
548 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 548 conjugacy classes of subgroups — too many to draw. Only its 131 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×#22548739 | C2 | semidirect |
| 2. #30632235 | C2 | semidirect |
| 3. C4×D4×D251 | C2 | semidirect |
| 4. #30631901 | C2 | semidirect |
| 5. #30631900 | C2 | semidirect |
| 6. #30631893 | C2 | semidirect |
| 7. #30631892 | C2 | semidirect |
| 8. #30631879 | C2 | semidirect |
| 9. #30631709 | C2 | semidirect |
| 10. #30631685 | C2 | semidirect |
| 11. #459×C251 | C2 | semidirect |
| 20. #22548715 | C22 | semidirect |
| 21. #22548702 | C22 | semidirect |
| 34. C4⋊(C251⋊C8) | C22 | semidirect |
| 35. Dic251⋊C8 | C22 | semidirect |
| 36. #22548640 | C22 | semidirect |
| 37. #22548638 | C22 | semidirect |
| 38. #22548636 | C22 | semidirect |
| 40. #127×C251 | C22 | semidirect |
| 42. C4⋊C8×C251 | C22 | semidirect |
| 43. #102×C251 | C22 | semidirect |
| 52. D4×D251 | D4 | semidirect |
| 145. C4×C251 | AGL(1,ℤ/8) | semidirect |
| 160. C251 | #3036 | semidirect |
| 170. #459 | D251 | semidirect |
| 183. #127 | C2×D251 | semidirect |
| 200. C4⋊C8 | C2×D251 | semidirect |
| 204. #102 | C2×D251 | semidirect |
| 311. C4 | #22548739 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22548739 | 2 |
| #30632235 | 2 |
| C4×D4×D251 | 2 |
| #30631901 | 2 |
| #30631900 | 2 |
| #30631893 | 2 |
| #30631892 | 2 |
| #30631879 | 2 |
| #30631709 | 2 |
| #30631685 | 2 |
| #459×C251 | 2 |
| #3036 | 251 |