Finite Group DatabasebetaFinite Group DatabasebetaOrder 14464.
398 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 398 conjugacy classes of subgroups — too many to draw. Only its 133 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. #20299229 | C2 | semidirect |
| 3. #20298901 | C2 | semidirect |
| 4. #20298897 | C2 | semidirect |
| 5. #20298887 | C2 | semidirect |
| 6. #20298877 | C2 | semidirect |
| 7. #20298634 | C2 | semidirect |
| 8. #20298626 | C2 | semidirect |
| 11. #428×C113 | C2 | semidirect |
| 15. #16813621 | C22 | semidirect |
| 17. #16813613 | C22 | semidirect |
| 26. #16813555 | C22 | semidirect |
| 27. #16813555 | C22 | semidirect |
| 28. #16813553 | C22 | semidirect |
| 29. #16813553 | C22 | semidirect |
| 30. #16813551 | C22 | semidirect |
| 31. #16813551 | C22 | semidirect |
| 39. #107×C113 | C22 | semidirect |
| 40. #106×C113 | C22 | semidirect |
| 45. C2×D452 | Q8 | semidirect |
| 125. C113 | #3081 | semidirect |
| 132. #428 | D113 | semidirect |
| 156. #107 | C2×D113 | semidirect |
| 159. #106 | C2×D113 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20299229 | 2 |
| #20299072 | 2 |
| #20298901 | 2 |
| #20298897 | 2 |
| #20298887 | 2 |
| #20298877 | 2 |
| #20298634 | 2 |
| #20298626 | 2 |
| #20298604 | 2 |
| C2×#16813542 | 2 |
| #428×C113 | 2 |
| #3081 | 113 |