Finite Group DatabasebetaFinite Group DatabasebetaOrder 14464.
532 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 532 conjugacy classes of subgroups — too many to draw. Only its 125 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. #20299146 | C2 | semidirect |
| 2. #127×D113 | C2 | semidirect |
| 3. #20298974 | C2 | semidirect |
| 4. #20298945 | C2 | semidirect |
| 5. #20298944 | C2 | semidirect |
| 6. #20298791 | C2 | semidirect |
| 7. #20298730 | C2 | semidirect |
| 8. #20298649 | C2 | semidirect |
| 9. #493×C113 | C2 | semidirect |
| 14. C2×#14268632 | C22 | semidirect |
| 15. #16813622 | C22 | semidirect |
| 24. D4×Dic113 | C22 | semidirect |
| 26. #16813551 | C22 | semidirect |
| 27. #16813544 | C22 | semidirect |
| 28. #16813543 | C22 | semidirect |
| 30. C4×#11744751 | C22 | semidirect |
| 31. C2×D8×C113 | C22 | semidirect |
| 33. #127×C113 | C22 | semidirect |
| 34. C4×C8×C113 | C22 | semidirect |
| 100. C4×D113 | D8 | semidirect |
| 133. C113 | #3205 | semidirect |
| 137. #493 | D113 | semidirect |
| 148. C2×D8 | C2×D113 | semidirect |
| 155. #127 | C2×D113 | semidirect |
| 167. C4×C8 | C2×D113 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20299146 | 2 |
| #127×D113 | 2 |
| #20298974 | 2 |
| #20298945 | 2 |
| #20298944 | 2 |
| #20298791 | 2 |
| #20298730 | 2 |
| #20298649 | 2 |
| #493×C113 | 2 |
| #3205 | 113 |