Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
240 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 240 conjugacy classes of subgroups — too many to draw. Only its 77 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 |
|---|---|---|
| 47. C4⋊Dic97 | C8 | semidirect |
| 48. #13095490 | C8 | semidirect |
| 49. #13095490 | C8 | semidirect |
| 50. C4⋊C4×C97 | C8 | semidirect |
| 111. C97 | #1916 | semidirect |
| 155. C4⋊C4 | #11715906 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4⋊#11715906 | 2 |
| C2×C4×#11715906 | 2 |
| (C2×#11715906)⋊C4 | 2 |
| C4⋊C4×#87604 | 2 |
| #1916 | 97 |