Finite Group DatabasebetaFinite Group DatabasebetaOrder 14464.
516 conjugacy classes of subgroups; only the 189 normal subgroups are shown.
This group has 516 conjugacy classes of subgroups — too many to draw. Only its 189 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. #20298480 | C2 | semidirect |
| 4. #20298449 | C2 | semidirect |
| 6. C42×Dic113 | C2 | semidirect |
| 7. #383×C113 | C2 | semidirect |
| 9. #16813616 | C4 | semidirect |
| 28. #14268626 | C2×C4 | semidirect |
| 37. C42×C113 | C2×C4 | semidirect |
| 68. Dic113 | #126 | semidirect |
| 74. C113 | C4×#126 | semidirect |
| 78. #383 | D113 | semidirect |
| 111. C42 | C4×D113 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16813616 | 2 |
| #20298487 | 2 |
| #20298480 | 2 |
| #20298449 | 2 |
| #20298445 | 2 |
| C42×Dic113 | 2 |
| #383×C113 | 2 |
| C4×#126 | 113 |