Finite Group DatabasebetaFinite Group DatabasebetaOrder 14464.
584 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 584 conjugacy classes of subgroups — too many to draw. Only its 157 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. C22×#14268636 | C2 | semidirect |
| 2. C22×#14268635 | C2 | semidirect |
| 4. C2×#16813587 | C2 | semidirect |
| 5. #20298797 | C2 | direct (N × H) |
| 6. C2×#16813551 | C2 | semidirect |
| 7. C2×#16813542 | C2 | semidirect |
| 8. C2×#102×C113 | C2 | semidirect |
| 14. C2×#14268636 | C22 | semidirect |
| 16. C2×#14268635 | C22 | semidirect |
| 21. #16813587 | C22 | semidirect |
| 25. #16813551 | C22 | semidirect |
| 26. #16813542 | C22 | semidirect |
| 30. #102×C113 | C22 | semidirect |
| 34. C2×Dic226 | D4 | semidirect |
| 89. C2×Dic113 | SD16 | semidirect |
| 97. Dic226 | C2×D4 | semidirect |
| 118. Dic113 | C2×SD16 | semidirect |
| 120. C2×C113 | #460 | semidirect |
| 126. C113 | C2×#460 | semidirect |
| 134. C2×#102 | D113 | semidirect |
| 156. #102 | C2×D113 | semidirect |
| 247. C2 | #20298797 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14268636 | 2 |
| C22×#14268635 | 2 |
| C2×#16813618 | 2 |
| C2×#16813587 | 2 |
| #20298797 | 2 |
| C2×#16813551 | 2 |
| C2×#16813542 | 2 |
| C2×#102×C113 | 2 |
| C2×#460 | 113 |