Finite Group DatabasebetaFinite Group DatabasebetaOrder 14464.
372 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 372 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. #20299229 | C2 | semidirect |
| 3. #20298965 | C2 | semidirect |
| 4. #20298959 | C2 | semidirect |
| 5. #20298954 | C2 | semidirect |
| 6. #20298947 | C2 | semidirect |
| 7. #20298607 | C2 | semidirect |
| 10. #20298553 | C2 | semidirect |
| 11. C2×#103×C113 | C2 | semidirect |
| 128. C113 | #3137 | semidirect |
| 138. C2×#103 | D113 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20299229 | 2 |
| #20299172 | 2 |
| #20298965 | 2 |
| #20298959 | 2 |
| #20298954 | 2 |
| #20298947 | 2 |
| #20298607 | 2 |
| #20298597 | 2 |
| #20298595 | 2 |
| #20298553 | 2 |
| C2×#103×C113 | 2 |
| #3137 | 113 |