Finite Group DatabasebetaFinite Group DatabasebetaOrder 14464.
398 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 398 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 |
|---|---|---|
| 2. #20298895 | C2 | semidirect |
| 3. #20298895 | C2 | semidirect |
| 4. #20298885 | C2 | semidirect |
| 5. #20298875 | C2 | semidirect |
| 6. #20298638 | C2 | semidirect |
| 7. #20298634 | C2 | semidirect |
| 8. #20298625 | C2 | semidirect |
| 11. #544×C113 | C2 | semidirect |
| 21. #16813555 | C22 | semidirect |
| 22. #16813555 | C22 | semidirect |
| 23. #16813555 | C22 | semidirect |
| 24. #16813553 | C22 | semidirect |
| 25. #16813553 | C22 | semidirect |
| 26. #16813553 | C22 | semidirect |
| 27. C4⋊#11744751 | C22 | semidirect |
| 28. C4⋊#11744751 | C22 | semidirect |
| 34. C4⋊Q8×C113 | C22 | semidirect |
| 36. #125×C113 | C22 | semidirect |
| 44. C2×D452 | Q8 | semidirect |
| 125. C113 | #3081 | semidirect |
| 126. #544 | D113 | semidirect |
| 141. C4⋊Q8 | C2×D113 | semidirect |
| 143. #125 | C2×D113 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20299072 | 2 |
| #20298895 | 2 |
| #20298885 | 2 |
| #20298875 | 2 |
| #20298638 | 2 |
| #20298634 | 2 |
| #20298625 | 2 |
| #20298602 | 2 |
| C2×#16813542 | 2 |
| #544×C113 | 2 |
| #3081 | 113 |