Finite Group DatabasebetaFinite Group DatabasebetaOrder 14464.
516 conjugacy classes of subgroups; only the 205 normal subgroups are shown.
This group has 516 conjugacy classes of subgroups — too many to draw. Only its 205 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. #20298482 | C2 | semidirect |
| 4. #20298466 | C2 | semidirect |
| 5. C4×#14268626 | C2 | semidirect |
| 7. C43×C113 | C2 | semidirect |
| 9. #16813616 | C4 | direct (N × H) |
| 28. #14268626 | C2×C4 | semidirect |
| 37. C42×C113 | C2×C4 | semidirect |
| 65. C4×C113 | #126 | semidirect |
| 74. C113 | C4×#126 | semidirect |
| 81. C43 | D113 | semidirect |
| 111. C42 | C4×D113 | semidirect |
| 142. C4 | #16813616 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16813616 | 2 |
| #20298489 | 2 |
| #20298482 | 2 |
| #20298466 | 2 |
| C4×#14268626 | 2 |
| C4×#14268624 | 2 |
| C43×C113 | 2 |
| C4×#126 | 113 |