Finite Group DatabasebetaFinite Group DatabasebetaOrder 14464.
608 conjugacy classes of subgroups; only the 205 normal subgroups are shown.
This group has 608 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 |
|---|---|---|
| 2. C2×C4×D452 | C2 | semidirect |
| 3. #20298708 | C2 | direct (N × H) |
| 4. C2×#16813553 | C2 | semidirect |
| 5. C2×#16813543 | C2 | semidirect |
| 6. C2×#16813542 | C2 | semidirect |
| 7. C2×#16813533 | C2 | semidirect |
| 8. C2×C4×D4×C113 | C2 | semidirect |
| 11. C2×#14268632 | C4 | semidirect |
| 16. C4×D452 | C22 | semidirect |
| 19. #16813553 | C22 | semidirect |
| 20. #16813543 | C22 | semidirect |
| 21. #16813542 | C22 | semidirect |
| 22. #16813533 | C22 | semidirect |
| 26. C4×D4×C113 | C22 | semidirect |
| 33. C2×D452 | C2×C4 | semidirect |
| 38. #14268632 | C2×C4 | semidirect |
| 40. C2×#11744751 | C2×C4 | semidirect |
| 49. C2×D4×C113 | C2×C4 | semidirect |
| 73. D4×C113 | C22×C4 | semidirect |
| 89. D452 | C22×C4 | semidirect |
| 92. #11744751 | C22×C4 | semidirect |
| 113. C2×C113 | #442 | semidirect |
| 119. C113 | C2×#442 | semidirect |
| 122. C2×C4×D4 | D113 | semidirect |
| 139. C4×D4 | C2×D113 | semidirect |
| 157. C2×D4 | C4×D113 | semidirect |
| 195. D4 | C2×C4×D113 | semidirect |
| 233. C2 | #20298708 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14268632 | 2 |
| C2×C4×D452 | 2 |
| #20298708 | 2 |
| C2×#16813553 | 2 |
| C2×#16813543 | 2 |
| C2×#16813542 | 2 |
| C2×#16813533 | 2 |
| C2×C4×D4×C113 | 2 |
| C2×#442 | 113 |