Finite Group DatabasebetaFinite Group DatabasebetaOrder 14464.
856 conjugacy classes of subgroups; only the 218 normal subgroups are shown.
This group has 856 conjugacy classes of subgroups — too many to draw. Only its 218 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. C22×#14268657 | C2 | semidirect |
| 2. C22×C4×#90673 | C2 | semidirect |
| 3. C2×#16813687 | C2 | direct (N × H) |
| 7. C2×#14268657 | C22 | semidirect |
| 10. C2×C4×#90673 | C22 | semidirect |
| 11. #16813687 | C22 | direct (N × H) |
| 14. C2×#14268648 | C4 | semidirect |
| 17. C22×D452 | C4 | semidirect |
| 20. C22×Q8×C113 | C4 | semidirect |
| 24. #14268657 | C23 | semidirect |
| 27. C4×#90673 | C23 | semidirect |
| 33. #14268648 | C2×C4 | semidirect |
| 38. C2×D452 | C2×C4 | semidirect |
| 47. C2×Q8×C113 | C2×C4 | semidirect |
| 59. Q8×C113 | C22×C4 | semidirect |
| 68. D452 | C22×C4 | semidirect |
| 77. C22×C113 | #104 | semidirect |
| 91. C2×C113 | C2×#104 | semidirect |
| 97. C113 | C22×#104 | semidirect |
| 106. C22×Q8 | #90673 | semidirect |
| 126. C2×Q8 | C2×#90673 | semidirect |
| 154. Q8 | C22×#90673 | semidirect |
| 180. C22 | #16813687 | direct (N × H) |
| 191. C2 | C2×#16813687 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14268657 | 2 |
| C22×C4×#90673 | 2 |
| C2×#16813687 | 2 |
| C22×#14268648 | 2 |
| C22×#104 | 113 |