Finite Group DatabasebetaFinite Group DatabasebetaOrder 14464.
564 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 564 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×#14268634 | C2 | semidirect |
| 3. C2×C4×D452 | C2 | semidirect |
| 4. #20298810 | C2 | direct (N × H) |
| 5. C2×C4⋊#11744751 | C2 | semidirect |
| 6. C2×#16813546 | C2 | semidirect |
| 7. C2×#16813543 | C2 | semidirect |
| 8. C2×#124×C113 | C2 | semidirect |
| 12. C2×#14268634 | C22 | semidirect |
| 18. C4×D452 | C22 | semidirect |
| 21. C4⋊#11744751 | C22 | semidirect |
| 22. #16813546 | C22 | semidirect |
| 23. #16813543 | C22 | semidirect |
| 27. #124×C113 | C22 | semidirect |
| 118. C2×C113 | #463 | semidirect |
| 124. C113 | C2×#463 | semidirect |
| 127. C2×#124 | D113 | semidirect |
| 144. #124 | C2×D113 | semidirect |
| 243. C2 | #20298810 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14268634 | 2 |
| C22×#14268632 | 2 |
| C2×C4×D452 | 2 |
| #20298810 | 2 |
| C2×C4⋊#11744751 | 2 |
| C2×#16813546 | 2 |
| C2×#16813543 | 2 |
| C2×#124×C113 | 2 |
| C2×#463 | 113 |