Finite Group DatabasebetaFinite Group DatabasebetaOrder 14464.
1504 conjugacy classes of subgroups; only the 525 normal subgroups are shown.
This group has 1504 conjugacy classes of subgroups — too many to draw. Only its 525 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×#14268648 | C2 | semidirect |
| 2. C22×#14268646 | C2 | semidirect |
| 3. C2×#16813643 | C2 | direct (N × H) |
| 4. C22×#14268637 | C2 | semidirect |
| 5. C22×#14268636 | C2 | semidirect |
| 6. C22×#14268632 | C2 | semidirect |
| 7. C22×C8×D113 | C2 | semidirect |
| 8. C22×SD16×C113 | C2 | semidirect |
| 10. C2×#14268648 | C22 | semidirect |
| 12. C2×#14268646 | C22 | semidirect |
| 20. #16813643 | C22 | direct (N × H) |
| 21. C2×#14268637 | C22 | semidirect |
| 22. C2×#14268636 | C22 | semidirect |
| 23. C2×#14268632 | C22 | semidirect |
| 25. C2×C8×D113 | C22 | semidirect |
| 28. C2×SD16×C113 | C22 | semidirect |
| 33. #14268648 | C23 | semidirect |
| 35. #14268646 | C23 | semidirect |
| 48. #14268637 | C23 | semidirect |
| 49. #14268636 | C23 | semidirect |
| 50. #14268632 | C23 | semidirect |
| 52. C8×D113 | C23 | semidirect |
| 60. SD16×C113 | C23 | semidirect |
| 92. C22×C113 | #135 | semidirect |
| 104. C2×C113 | C2×#135 | semidirect |
| 109. C113 | C22×#135 | semidirect |
| 115. C22×SD16 | D113 | semidirect |
| 134. C2×SD16 | C2×D113 | semidirect |
| 166. SD16 | C22×D113 | semidirect |
| 205. C22 | #16813643 | direct (N × H) |
| 215. C2 | C2×#16813643 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14268648 | 2 |
| C22×#14268646 | 2 |
| C2×#16813643 | 2 |
| C22×#14268637 | 2 |
| C22×#14268636 | 2 |
| C22×#14268632 | 2 |
| C22×C8×D113 | 2 |
| C22×SD16×C113 | 2 |
| C22×#135 | 113 |