Finite Group DatabasebetaFinite Group DatabasebetaOrder 14464.
488 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 488 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. #20299153 | C2 | semidirect |
| 3. #20298972 | C2 | semidirect |
| 4. #20298945 | C2 | semidirect |
| 5. #20298944 | C2 | semidirect |
| 6. #20298796 | C2 | semidirect |
| 7. #20298747 | C2 | semidirect |
| 8. #20298649 | C2 | semidirect |
| 9. #492×C113 | C2 | semidirect |
| 13. C2×#14268634 | C22 | semidirect |
| 14. #16813622 | C22 | semidirect |
| 22. Q8×Dic113 | C22 | semidirect |
| 26. #16813551 | C22 | semidirect |
| 27. #16813544 | C22 | semidirect |
| 28. #16813543 | C22 | semidirect |
| 30. C4×#11744751 | C22 | semidirect |
| 31. C2×SD16×C113 | C22 | semidirect |
| 32. C4⋊Q8×C113 | C22 | semidirect |
| 34. C4×C8×C113 | C22 | semidirect |
| 95. C4×D113 | SD16 | semidirect |
| 125. C113 | #3208 | semidirect |
| 129. #492 | D113 | semidirect |
| 139. C2×SD16 | C2×D113 | semidirect |
| 141. C4⋊Q8 | C2×D113 | semidirect |
| 159. C4×C8 | C2×D113 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20299153 | 2 |
| #127×D113 | 2 |
| #20298972 | 2 |
| #20298945 | 2 |
| #20298944 | 2 |
| #20298796 | 2 |
| #20298747 | 2 |
| #20298649 | 2 |
| #492×C113 | 2 |
| #3208 | 113 |