Finite Group DatabasebetaFinite Group DatabasebetaOrder 14464.
224 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 224 conjugacy classes of subgroups — too many to draw. Only its 101 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. #20299682 | C2 | semidirect |
| 4. C8×#11744762 | C2 | semidirect |
| 24. #14268657 | C8 | semidirect |
| 25. #14268656 | C8 | semidirect |
| 32. #14268631 | C8 | semidirect |
| 33. #14268630 | C8 | semidirect |
| 35. M16×C113 | C8 | semidirect |
| 45. #11744762 | M16 | direct (N × H) |
| 52. #11744753 | C2×C8 | semidirect |
| 53. C8×C113 | C2×C8 | semidirect |
| 54. #11744751 | C2×C8 | semidirect |
| 74. C113 | C8×M16 | semidirect |
| 99. M16 | #11744762 | direct (N × H) |
| 128. C8 | C2×#11744762 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20299711 | 2 |
| C2×C4×#11744762 | 2 |
| #20299682 | 2 |
| C8×#11744762 | 2 |
| M16×#90673 | 2 |
| C8×M16 | 113 |