Finite Group DatabasebetaFinite Group DatabasebetaOrder 14464.
472 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 472 conjugacy classes of subgroups — too many to draw. Only its 125 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×#16813651 | C2 | semidirect |
| 2. #20299263 | C2 | semidirect |
| 4. #20298977 | C2 | semidirect |
| 5. #20298855 | C2 | semidirect |
| 6. #20298809 | C2 | semidirect |
| 7. #20298757 | C2 | semidirect |
| 8. #20298755 | C2 | semidirect |
| 9. C4×#14268635 | C2 | semidirect |
| 10. #20298675 | C2 | semidirect |
| 11. #461×C113 | C2 | semidirect |
| 57. #14268635 | D4 | semidirect |
| 122. C4×C113 | #137 | semidirect |
| 135. C113 | #3276 | semidirect |
| 142. #461 | D113 | semidirect |
| 261. C4 | #16813651 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16813651 | 2 |
| #20299263 | 2 |
| #20299252 | 2 |
| #20298977 | 2 |
| #20298855 | 2 |
| #20298809 | 2 |
| #20298757 | 2 |
| #20298755 | 2 |
| C4×#14268635 | 2 |
| #20298675 | 2 |
| #461×C113 | 2 |
| #3276 | 113 |