Finite Group DatabasebetaFinite Group DatabasebetaOrder 14464.
368 conjugacy classes of subgroups; only the 191 normal subgroups are shown.
This group has 368 conjugacy classes of subgroups — too many to draw. Only its 191 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. #20299719 | C2 | direct (N × H) |
| 2. C2×#16813719 | C2 | semidirect |
| 3. C2×#16813718 | C2 | semidirect |
| 4. C2×#16813717 | C2 | semidirect |
| 5. C22×#14268659 | C2 | semidirect |
| 7. #16813719 | C22 | semidirect |
| 8. #16813718 | C22 | semidirect |
| 9. #16813717 | C22 | semidirect |
| 13. C2×#14268659 | C22 | semidirect |
| 66. C2×C113 | #504 | semidirect |
| 70. C113 | C2×#504 | semidirect |
| 137. C2 | #20299719 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20299719 | 2 |
| C2×#16813719 | 2 |
| C2×#16813718 | 2 |
| C2×#16813717 | 2 |
| C22×#14268659 | 2 |
| C2×#16813709 | 2 |
| C2×#504 | 113 |