Finite Group DatabasebetaFinite Group DatabasebetaOrder 14464.
392 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 392 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. #20299151 | C2 | semidirect |
| 3. #20298965 | C2 | semidirect |
| 4. #20298961 | C2 | semidirect |
| 5. #20298959 | C2 | semidirect |
| 6. #20298956 | C2 | semidirect |
| 7. #20298595 | C2 | semidirect |
| 8. #20298594 | C2 | semidirect |
| 9. #20298592 | C2 | semidirect |
| 10. C2×#16813532 | C2 | semidirect |
| 11. #416×C113 | C2 | semidirect |
| 126. C113 | #3135 | semidirect |
| 136. #416 | D113 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20299151 | 2 |
| #20299144 | 2 |
| #20298965 | 2 |
| #20298961 | 2 |
| #20298959 | 2 |
| #20298956 | 2 |
| #20298595 | 2 |
| #20298594 | 2 |
| #20298592 | 2 |
| C2×#16813532 | 2 |
| #416×C113 | 2 |
| #3135 | 113 |