Finite Group DatabasebetaFinite Group DatabasebetaOrder 14464.
526 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 526 conjugacy classes of subgroups — too many to draw. Only its 141 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. #20299165 | C2 | semidirect |
| 3. #20299073 | C2 | semidirect |
| 4. #20298811 | C2 | semidirect |
| 5. #20298791 | C2 | semidirect |
| 6. #20298624 | C2 | semidirect |
| 7. #20298603 | C2 | semidirect |
| 8. #20298595 | C2 | semidirect |
| 9. C22×D8×C113 | C2 | semidirect |
| 12. C2×#14268635 | C22 | semidirect |
| 13. C2×#14268632 | C22 | semidirect |
| 15. #16813618 | C22 | semidirect |
| 16. #16813609 | C22 | semidirect |
| 20. D4×Dic113 | C22 | semidirect |
| 24. #16813551 | C22 | semidirect |
| 25. #16813547 | C22 | semidirect |
| 26. #16813544 | C22 | semidirect |
| 27. #16813543 | C22 | semidirect |
| 60. C2×D4×C113 | D4 | semidirect |
| 122. C113 | #3041 | semidirect |
| 124. C22×D8 | D113 | semidirect |
| 168. 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×#16813648 | 2 |
| #20299165 | 2 |
| #20299073 | 2 |
| #20298811 | 2 |
| #20298791 | 2 |
| #20298624 | 2 |
| #20298603 | 2 |
| #20298595 | 2 |
| C22×D8×C113 | 2 |
| #3041 | 113 |