Finite Group DatabasebetaFinite Group DatabasebetaOrder 14464.
386 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 386 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 |
|---|---|---|
| 2. #20298936 | C2 | semidirect |
| 3. #20298890 | C2 | semidirect |
| 4. #20298885 | C2 | semidirect |
| 5. #20298805 | C2 | semidirect |
| 6. #20298800 | C2 | semidirect |
| 8. #20298703 | C2 | semidirect |
| 9. #20298696 | C2 | semidirect |
| 10. #20298655 | C2 | semidirect |
| 11. #533×C113 | C2 | semidirect |
| 137. C113 | #3116 | semidirect |
| 138. #533 | D113 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#14268647 | 2 |
| #20298936 | 2 |
| #20298890 | 2 |
| #20298885 | 2 |
| #20298805 | 2 |
| #20298800 | 2 |
| #20298758 | 2 |
| #20298703 | 2 |
| #20298696 | 2 |
| #20298655 | 2 |
| #533×C113 | 2 |
| #3116 | 113 |