Finite Group DatabasebetaFinite Group DatabasebetaOrder 14464.
456 conjugacy classes of subgroups; only the 197 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 197 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 |
|---|---|---|
| 1. Q8×#11744762 | C2 | semidirect |
| 2. D4×#11744762 | C2 | semidirect |
| 3. #20299711 | C2 | semidirect |
| 4. C2×C4×#11744762 | C2 | semidirect |
| 31. #14268648 | C8 | semidirect |
| 32. #14268647 | C8 | semidirect |
| 33. #14268646 | C8 | semidirect |
| 37. #41×C113 | C8 | semidirect |
| 46. #11744762 | #41 | direct (N × H) |
| 47. Q8×C113 | C2×C8 | semidirect |
| 48. D4×C113 | C2×C8 | semidirect |
| 49. C2×C4×C113 | C2×C8 | semidirect |
| 50. C22⋊D113 | C2×C8 | semidirect |
| 51. C2×Dic113 | C2×C8 | semidirect |
| 52. D452 | C2×C8 | semidirect |
| 53. C4×D113 | C2×C8 | semidirect |
| 54. C4×D113 | C2×C8 | semidirect |
| 57. Dic226 | C2×C8 | semidirect |
| 77. C113 | C8×#41 | semidirect |
| 99. #41 | #11744762 | direct (N × H) |
| 117. Q8 | C2×#11744762 | semidirect |
| 120. D4 | C2×#11744762 | semidirect |
| 132. C2×C4 | C2×#11744762 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×#11744762 | 2 |
| D4×#11744762 | 2 |
| #20299711 | 2 |
| C2×C4×#11744762 | 2 |
| #41×#90673 | 2 |
| C8×#41 | 113 |