Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
526 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 526 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. C22×#13095496 | C2 | semidirect |
| 2. #20261299 | C2 | semidirect |
| 3. #20261210 | C2 | semidirect |
| 4. #20260952 | C2 | semidirect |
| 5. #20260928 | C2 | semidirect |
| 6. #20260763 | C2 | semidirect |
| 7. #20260741 | C2 | semidirect |
| 8. #20260731 | C2 | semidirect |
| 9. C2×AGL(1,ℤ/8)×C97 | C2 | semidirect |
| 14. #15690806 | C22 | semidirect |
| 15. #15690799 | C22 | semidirect |
| 19. D4×Dic97 | C22 | semidirect |
| 23. #15690739 | C22 | semidirect |
| 24. #15690734 | C22 | semidirect |
| 25. #15690732 | C22 | semidirect |
| 26. #15690731 | C22 | semidirect |
| 30. C2×SD16×C97 | C22 | semidirect |
| 31. C2×D8×C97 | C22 | semidirect |
| 58. C2×D4×C97 | D4 | semidirect |
| 122. C97 | #3041 | semidirect |
| 123. C2×AGL(1,ℤ/8) | D97 | semidirect |
| 136. C2×SD16 | C2×D97 | semidirect |
| 139. C2×D8 | C2×D97 | semidirect |
| 168. C2×D4 | C22⋊D97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13095496 | 2 |
| #20261299 | 2 |
| #20261210 | 2 |
| #20260952 | 2 |
| #20260928 | 2 |
| #20260763 | 2 |
| #20260741 | 2 |
| #20260731 | 2 |
| C2×AGL(1,ℤ/8)×C97 | 2 |
| #3041 | 97 |