Finite Group DatabasebetaFinite Group DatabasebetaOrder 14464.
424 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 424 conjugacy classes of subgroups — too many to draw. Only its 113 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. #20299111 | C2 | semidirect |
| 2. #20298938 | C2 | semidirect |
| 3. #20298925 | C2 | semidirect |
| 4. #20298834 | C2 | semidirect |
| 5. #20298829 | C2 | semidirect |
| 6. #20298759 | C2 | semidirect |
| 7. #20298746 | C2 | semidirect |
| 8. C2×#16813534 | C2 | semidirect |
| 9. #467×C113 | C2 | semidirect |
| 12. C2×#14268634 | C22 | semidirect |
| 13. C2×D904 | C22 | semidirect |
| 23. #16813556 | C22 | semidirect |
| 24. #16813553 | C22 | semidirect |
| 25. #16813546 | C22 | semidirect |
| 26. #16813544 | C22 | semidirect |
| 27. #16813542 | C22 | semidirect |
| 30. C2×Q16×C113 | C22 | semidirect |
| 33. #107×C113 | C22 | semidirect |
| 34. #103×C113 | C22 | semidirect |
| 122. C113 | #3191 | semidirect |
| 126. #467 | D113 | semidirect |
| 134. C2×Q16 | C2×D113 | semidirect |
| 149. #107 | C2×D113 | semidirect |
| 152. #103 | C2×D113 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20299111 | 2 |
| #20298938 | 2 |
| #20298925 | 2 |
| #20298834 | 2 |
| #20298829 | 2 |
| #20298759 | 2 |
| #20298746 | 2 |
| C2×#16813534 | 2 |
| #467×C113 | 2 |
| #3191 | 113 |