Finite Group DatabasebetaFinite Group DatabasebetaOrder 14464.
216 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 119 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. #20299691 | C2 | direct (N × H) |
| 4. #16813717 | C4 | semidirect |
| 6. C2×#14268659 | C4 | semidirect |
| 12. #14268659 | C2×C4 | semidirect |
| 26. C2×#90673 | C16 | semidirect |
| 42. #90673 | C2×C16 | semidirect |
| 47. C2×C113 | C4×C16 | semidirect |
| 49. D113 | C4×C16 | semidirect |
| 52. C113 | C2×C4×C16 | semidirect |
| 101. C2 | #20299691 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16813717 | 2 |
| #20299691 | 2 |
| C2×C8×#90673 | 2 |
| C2×C4×C16 | 113 |