Finite Group DatabasebetaFinite Group DatabasebetaOrder 14464.
656 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 656 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. C2×#16813648 | C2 | semidirect |
| 2. #20299148 | C2 | semidirect |
| 3. #20298985 | C2 | semidirect |
| 4. #20298974 | C2 | semidirect |
| 5. #20298970 | C2 | semidirect |
| 6. C4×#14268631 | C2 | semidirect |
| 7. C2×#127×C113 | C2 | semidirect |
| 10. C2×#14268635 | C22 | semidirect |
| 11. C2×#14268632 | C22 | semidirect |
| 13. #16813622 | C22 | semidirect |
| 14. #16813619 | C22 | semidirect |
| 15. #16813610 | C22 | semidirect |
| 18. #16813533 | C22 | semidirect |
| 19. C4×#11744751 | C22 | semidirect |
| 34. #14268631 | D4 | semidirect |
| 71. #11744751 | C2×D4 | semidirect |
| 82. C4×C113 | AGL(1,ℤ/8) | semidirect |
| 91. C113 | #3151 | semidirect |
| 94. C2×#127 | D113 | semidirect |
| 174. C4 | #16813648 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16813648 | 2 |
| #20299148 | 2 |
| #20298985 | 2 |
| #20298974 | 2 |
| #20298970 | 2 |
| C4×#14268631 | 2 |
| C2×#127×C113 | 2 |
| #3151 | 113 |