Finite Group DatabasebetaFinite Group DatabasebetaOrder 14464.
444 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 444 conjugacy classes of subgroups — too many to draw. Only its 121 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×#16813610 | C2 | semidirect |
| 2. #20298985 | C2 | semidirect |
| 3. #20298960 | C2 | semidirect |
| 4. #20298813 | C2 | semidirect |
| 5. #20298736 | C2 | semidirect |
| 6. #20298731 | C2 | semidirect |
| 7. #20298655 | C2 | semidirect |
| 8. #532×C113 | C2 | semidirect |
| 11. C2×#14268635 | C22 | semidirect |
| 19. C4⋊#11744751 | C22 | semidirect |
| 20. #16813545 | C22 | semidirect |
| 23. #16813533 | C22 | semidirect |
| 25. C4⋊Q8×C113 | C22 | semidirect |
| 26. #127×C113 | C22 | semidirect |
| 31. C4×D4×C113 | C22 | semidirect |
| 121. C113 | #3213 | semidirect |
| 122. #532 | D113 | semidirect |
| 135. C4⋊Q8 | C2×D113 | semidirect |
| 136. #127 | C2×D113 | semidirect |
| 145. C4×D4 | C2×D113 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16813610 | 2 |
| #20298985 | 2 |
| #20298960 | 2 |
| #20298813 | 2 |
| #20298736 | 2 |
| #20298731 | 2 |
| #20298655 | 2 |
| #532×C113 | 2 |
| #3213 | 113 |