Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
1880 conjugacy classes of subgroups; only the 901 normal subgroups are shown.
This group has 1880 conjugacy classes of subgroups — too many to draw. Only its 901 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 |
|---|---|---|
| 2. C2×#15690766 | C2 | direct (N × H) |
| 3. C22×#13095490 | C2 | semidirect |
| 5. C22×C4×Dic97 | C2 | semidirect |
| 7. C23×Dic97 | C4 | semidirect |
| 12. #15690766 | C22 | direct (N × H) |
| 13. C2×#13095490 | C22 | semidirect |
| 15. C2×C4×Dic97 | C22 | semidirect |
| 22. C22×Dic97 | C2×C4 | semidirect |
| 27. #13095490 | C23 | semidirect |
| 29. C4×Dic97 | C23 | semidirect |
| 49. C2×Dic97 | C22×C4 | semidirect |
| 55. C22×C97 | #117 | semidirect |
| 65. C2×C97 | C2×#117 | semidirect |
| 69. C97 | C22×#117 | semidirect |
| 124. C22 | #15690766 | direct (N × H) |
| 134. C2 | C2×#15690766 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C24×Dic97 | 2 |
| C2×#15690766 | 2 |
| C22×#13095490 | 2 |
| C22×C22⋊Dic97 | 2 |
| C22×C4×Dic97 | 2 |
| C22×C22⋊C4×C97 | 2 |
| C22×#117 | 97 |