Finite Group DatabasebetaFinite Group DatabasebetaOrder 14464.
584 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 584 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×#16813647 | C2 | semidirect |
| 2. C2×#16813619 | C2 | semidirect |
| 3. #20298798 | C2 | semidirect |
| 4. #20298793 | C2 | semidirect |
| 5. #20298622 | C2 | semidirect |
| 6. #20298602 | C2 | semidirect |
| 7. C4×#41×C113 | C2 | semidirect |
| 11. C2×#14268634 | C22 | semidirect |
| 12. C2×#14268632 | C22 | semidirect |
| 17. C4⋊#11744751 | C22 | semidirect |
| 18. #16813542 | C22 | semidirect |
| 20. C4×Q8×C113 | C22 | semidirect |
| 22. C4×D4×C113 | C22 | semidirect |
| 40. #41×C113 | D4 | semidirect |
| 63. Q8×C113 | C2×D4 | semidirect |
| 66. D4×C113 | C2×D4 | semidirect |
| 96. C4×C113 | AGL(1,ℤ/8) | semidirect |
| 105. C113 | #3038 | semidirect |
| 108. C4×#41 | D113 | semidirect |
| 123. C4×Q8 | C2×D113 | semidirect |
| 125. C4×D4 | C2×D113 | semidirect |
| 134. #41 | D452 | semidirect |
| 168. Q8 | C2×D452 | semidirect |
| 176. D4 | C2×D452 | semidirect |
| 201. C4 | #16813647 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16813647 | 2 |
| C2×#16813619 | 2 |
| #20298798 | 2 |
| #20298793 | 2 |
| #20298622 | 2 |
| #20298602 | 2 |
| C4×#41×C113 | 2 |
| #3038 | 113 |