Finite Group DatabasebetaFinite Group DatabasebetaOrder 14464.
472 conjugacy classes of subgroups; only the 162 normal subgroups are shown.
This group has 472 conjugacy classes of subgroups — too many to draw. Only its 162 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. C2×#16813710 | C2 | semidirect |
| 2. C2×#16813709 | C2 | semidirect |
| 3. #20299641 | C2 | direct (N × H) |
| 4. C2×#16813692 | C2 | semidirect |
| 5. C2×#16813687 | C2 | semidirect |
| 6. C2×#16813686 | C2 | semidirect |
| 7. C2×C8×#90673 | C2 | semidirect |
| 10. #16813710 | C22 | semidirect |
| 12. #16813709 | C22 | semidirect |
| 21. #16813692 | C22 | semidirect |
| 22. #16813687 | C22 | semidirect |
| 23. #16813686 | C22 | semidirect |
| 24. C8×#90673 | C22 | semidirect |
| 27. #16813643 | C4 | semidirect |
| 29. C2×#14268637 | C4 | semidirect |
| 30. C2×#14268636 | C4 | semidirect |
| 31. C2×#14268632 | C4 | semidirect |
| 33. C2×SD16×C113 | C4 | semidirect |
| 66. #14268637 | C2×C4 | semidirect |
| 67. #14268636 | C2×C4 | semidirect |
| 68. #14268632 | C2×C4 | semidirect |
| 74. SD16×C113 | C2×C4 | semidirect |
| 127. C2×C113 | #443 | semidirect |
| 133. C113 | C2×#443 | semidirect |
| 148. C2×SD16 | #90673 | semidirect |
| 187. SD16 | C2×#90673 | semidirect |
| 263. C2 | #20299641 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16813710 | 2 |
| C2×#16813709 | 2 |
| #20299641 | 2 |
| C2×#16813692 | 2 |
| C2×#16813687 | 2 |
| C2×#16813686 | 2 |
| C2×C8×#90673 | 2 |
| C2×#16813643 | 2 |
| C2×#443 | 113 |