Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
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×#15690818 | C2 | semidirect |
| 2. #20261313 | C2 | semidirect |
| 3. #20261302 | C2 | semidirect |
| 4. #20260985 | C2 | semidirect |
| 5. #20260978 | C2 | semidirect |
| 6. #20260968 | C2 | semidirect |
| 7. #20260961 | C2 | semidirect |
| 8. #20260777 | C2 | semidirect |
| 9. #20260731 | C2 | semidirect |
| 10. C2×#15690731 | C2 | semidirect |
| 11. C2×AGL(1,ℤ/8)×C97 | C2 | semidirect |
| 14. C2×#13095494 | C22 | semidirect |
| 16. C2×C8×D97 | C22 | semidirect |
| 20. #15690786 | C22 | semidirect |
| 25. #15690781 | C22 | semidirect |
| 29. #15690744 | C22 | semidirect |
| 30. #15690742 | C22 | semidirect |
| 31. #15690734 | C22 | semidirect |
| 32. #15690734 | C22 | semidirect |
| 35. #15690731 | C22 | semidirect |
| 36. #15690731 | C22 | semidirect |
| 83. M16×C97 | D4 | semidirect |
| 152. C97 | #3062 | semidirect |
| 153. C2×AGL(1,ℤ/8) | D97 | semidirect |
| 220. M16 | C22⋊D97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15690818 | 2 |
| #20261313 | 2 |
| #20261302 | 2 |
| #20260985 | 2 |
| #20260978 | 2 |
| #20260968 | 2 |
| #20260961 | 2 |
| #20260777 | 2 |
| #20260731 | 2 |
| C2×#15690731 | 2 |
| C2×AGL(1,ℤ/8)×C97 | 2 |
| #3062 | 97 |