Finite Group DatabasebetaFinite Group DatabasebetaOrder 14464.
784 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 784 conjugacy classes of subgroups — too many to draw. Only its 165 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. C22×#14268632 | C2 | semidirect |
| 3. #20299162 | C2 | semidirect |
| 4. #20298743 | C2 | semidirect |
| 5. #20298732 | C2 | semidirect |
| 6. #20298603 | C2 | semidirect |
| 7. #20298594 | C2 | semidirect |
| 8. #20298565 | C2 | semidirect |
| 9. C2×H(5,𝔽2)×C113 | C2 | semidirect |
| 10. C22×D452 | C22 | semidirect |
| 12. C2×#14268634 | C22 | semidirect |
| 14. C2×#14268632 | C22 | semidirect |
| 15. C2×#14268632 | C22 | semidirect |
| 16. C2×#14268631 | C22 | semidirect |
| 17. C22×#11744751 | C22 | semidirect |
| 20. #16813596 | C22 | semidirect |
| 22. #16813581 | C22 | semidirect |
| 23. #16813546 | C22 | semidirect |
| 24. #16813543 | C22 | semidirect |
| 25. #16813543 | C22 | semidirect |
| 26. C22⋊#11744751 | C22 | semidirect |
| 32. C2×#41×C113 | C22 | semidirect |
| 36. C22×D4×C113 | C22 | semidirect |
| 62. #41×C113 | D4 | semidirect |
| 76. C2×D4×C113 | D4 | semidirect |
| 152. C113 | #3008 | semidirect |
| 153. C2×H(5,𝔽2) | D113 | semidirect |
| 167. C2×#41 | C2×D113 | semidirect |
| 172. C22×D4 | C2×D113 | semidirect |
| 198. #41 | C22⋊D113 | semidirect |
| 217. C2×D4 | C22⋊D113 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16813647 | 2 |
| C22×#14268632 | 2 |
| #20299162 | 2 |
| #20298743 | 2 |
| #20298732 | 2 |
| #20298603 | 2 |
| #20298594 | 2 |
| #20298565 | 2 |
| C2×H(5,𝔽2)×C113 | 2 |
| #3008 | 113 |