Finite Group DatabasebetaFinite Group DatabasebetaOrder 14464.
648 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 648 conjugacy classes of subgroups — too many to draw. Only its 157 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×D904 | C2 | semidirect |
| 2. C22×#14268632 | C2 | semidirect |
| 3. C2×#16813618 | C2 | semidirect |
| 4. C2×#16813584 | C2 | semidirect |
| 5. #20298792 | C2 | direct (N × H) |
| 6. C2×#16813551 | C2 | semidirect |
| 7. C2×#16813542 | C2 | semidirect |
| 8. C2×#102×C113 | C2 | semidirect |
| 15. C2×D904 | C22 | semidirect |
| 17. C2×#14268632 | C22 | semidirect |
| 20. #16813618 | C22 | semidirect |
| 22. #16813584 | C22 | semidirect |
| 25. #16813551 | C22 | semidirect |
| 26. #16813542 | C22 | semidirect |
| 30. #102×C113 | C22 | semidirect |
| 38. C2×D452 | D4 | semidirect |
| 92. C2×Dic113 | D8 | semidirect |
| 100. D452 | C2×D4 | semidirect |
| 125. Dic113 | C2×D8 | semidirect |
| 127. C2×C113 | #459 | semidirect |
| 134. C113 | C2×#459 | semidirect |
| 142. C2×#102 | D113 | semidirect |
| 164. #102 | C2×D113 | semidirect |
| 263. C2 | #20298792 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D904 | 2 |
| C22×#14268632 | 2 |
| C2×#16813618 | 2 |
| C2×#16813584 | 2 |
| #20298792 | 2 |
| C2×#16813551 | 2 |
| C2×#16813542 | 2 |
| C2×#102×C113 | 2 |
| C2×#459 | 113 |