Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
656 conjugacy classes of subgroups; only the 277 normal subgroups are shown.
This group has 656 conjugacy classes of subgroups — too many to draw. Only its 277 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 |
|---|---|---|
| 3. #20260631 | C2 | semidirect |
| 5. C4×#13095490 | C2 | semidirect |
| 8. #15690769 | C4 | semidirect |
| 26. C4⋊Dic97 | C2×C4 | semidirect |
| 31. C4×Dic97 | C2×C4 | semidirect |
| 49. C2×C4×C97 | C4⋊C4 | semidirect |
| 81. C97 | #2296 | semidirect |
| 136. C2×C4 | #13095490 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15690769 | 2 |
| C22×C4×Dic97 | 2 |
| #20260631 | 2 |
| #20260607 | 2 |
| C4×#13095490 | 2 |
| C2×#117×C97 | 2 |
| #2296 | 97 |