Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
504 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 504 conjugacy classes of subgroups — too many to draw. Only its 141 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×#15692263 | C2 | semidirect |
| 2. #20265755 | C2 | semidirect |
| 3. #20265744 | C2 | semidirect |
| 4. #20265427 | C2 | semidirect |
| 5. #20265420 | C2 | semidirect |
| 6. #20265410 | C2 | semidirect |
| 7. #20265403 | C2 | semidirect |
| 8. #20265219 | C2 | semidirect |
| 9. #20265173 | C2 | semidirect |
| 10. C2×#15692176 | C2 | semidirect |
| 11. C2×AGL(1,ℤ/8)×C101 | C2 | semidirect |
| 14. C2×#13108057 | C22 | semidirect |
| 16. C2×C8×D101 | C22 | semidirect |
| 20. #15692231 | C22 | semidirect |
| 25. #15692226 | C22 | semidirect |
| 29. #15692189 | C22 | semidirect |
| 30. #15692187 | C22 | semidirect |
| 31. #15692179 | C22 | semidirect |
| 32. #15692179 | C22 | semidirect |
| 35. #15692176 | C22 | semidirect |
| 36. #15692176 | C22 | semidirect |
| 83. M16×C101 | D4 | semidirect |
| 152. C101 | #3062 | semidirect |
| 153. C2×AGL(1,ℤ/8) | D101 | semidirect |
| 220. M16 | C22⋊D101 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15692263 | 2 |
| #20265755 | 2 |
| #20265744 | 2 |
| #20265427 | 2 |
| #20265420 | 2 |
| #20265410 | 2 |
| #20265403 | 2 |
| #20265219 | 2 |
| #20265173 | 2 |
| C2×#15692176 | 2 |
| C2×AGL(1,ℤ/8)×C101 | 2 |
| #3062 | 101 |