Finite Group DatabasebetaFinite Group DatabasebetaOrder 14464.
528 conjugacy classes of subgroups; only the 160 normal subgroups are shown.
This group has 528 conjugacy classes of subgroups — too many to draw. Only its 160 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. #20299665 | C2 | semidirect |
| 2. #20299639 | C2 | semidirect |
| 3. D8×#90673 | C2 | semidirect |
| 4. #20299608 | C2 | semidirect |
| 5. #20299590 | C2 | semidirect |
| 6. #20299561 | C2 | semidirect |
| 10. D4×#90673 | C22 | semidirect |
| 14. #16813691 | C22 | semidirect |
| 15. #16813690 | C22 | semidirect |
| 16. #16813684 | C22 | semidirect |
| 17. #16813676 | C22 | semidirect |
| 18. C8×#90673 | C22 | semidirect |
| 20. C2×D904 | C4 | semidirect |
| 21. C2×#14268632 | C4 | semidirect |
| 22. D8×D113 | C4 | semidirect |
| 23. D8×D113 | C4 | semidirect |
| 27. C2×D8×C113 | C4 | semidirect |
| 40. C2×D452 | C2×C4 | semidirect |
| 44. D4×D113 | C2×C4 | semidirect |
| 47. D904 | C2×C4 | semidirect |
| 48. D904 | C2×C4 | semidirect |
| 49. #14268632 | C2×C4 | semidirect |
| 50. #14268632 | C2×C4 | semidirect |
| 51. C2×#11744751 | C2×C4 | semidirect |
| 52. C8×D113 | C2×C4 | semidirect |
| 53. C8×D113 | C2×C4 | semidirect |
| 56. C2×D4×C113 | C2×C4 | semidirect |
| 57. D8×C113 | C2×C4 | semidirect |
| 58. D8×C113 | C2×C4 | semidirect |
| 59. C2×C8×C113 | C2×C4 | semidirect |
| 109. C113 | #2948 | semidirect |
| 124. C2×D8 | #90673 | semidirect |
| 144. C2×D4 | C2×#90673 | semidirect |
| 151. D8 | C2×#90673 | semidirect |
| 152. D8 | C2×#90673 | semidirect |
| 161. C2×C8 | C2×#90673 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20299665 | 2 |
| #20299639 | 2 |
| D8×#90673 | 2 |
| #20299608 | 2 |
| #20299590 | 2 |
| #20299561 | 2 |
| C2×D8×D113 | 2 |
| #2948 | 113 |