Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
466 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 466 conjugacy classes of subgroups — too many to draw. Only its 137 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. #20261533 | C2 | semidirect |
| 2. C2×#15690836 | C2 | semidirect |
| 3. #20261501 | C2 | semidirect |
| 4. #20261002 | C2 | semidirect |
| 5. #20260995 | C2 | semidirect |
| 6. #20260784 | C2 | semidirect |
| 7. #20260719 | C2 | semidirect |
| 8. C2×#15690727 | C2 | semidirect |
| 9. C2×AGL(1,ℤ/8)×C97 | C2 | semidirect |
| 11. #15690841 | C22 | semidirect |
| 15. #15690836 | C22 | semidirect |
| 21. #15690816 | C22 | semidirect |
| 26. #15690746 | C22 | semidirect |
| 27. #15690729 | C22 | semidirect |
| 28. #15690727 | C22 | semidirect |
| 29. #15690727 | C22 | semidirect |
| 34. C2×SD16×C97 | C22 | semidirect |
| 35. C2×D8×C97 | C22 | semidirect |
| 148. C97 | #3068 | semidirect |
| 151. C2×AGL(1,ℤ/8) | D97 | semidirect |
| 171. C2×SD16 | C2×D97 | semidirect |
| 173. C2×D8 | C2×D97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20261533 | 2 |
| C2×#15690836 | 2 |
| #20261501 | 2 |
| #20261002 | 2 |
| #20260995 | 2 |
| #20260784 | 2 |
| #20260719 | 2 |
| C2×#15690727 | 2 |
| C2×AGL(1,ℤ/8)×C97 | 2 |
| #3068 | 97 |