Finite Group DatabasebetaFinite Group DatabasebetaOrder 14464.
370 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 370 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. #20299132 | C2 | semidirect |
| 2. #20299000 | C2 | semidirect |
| 3. #20298982 | C2 | semidirect |
| 4. #20298953 | C2 | semidirect |
| 5. #20298856 | C2 | semidirect |
| 7. #20298844 | C2 | semidirect |
| 8. #20298711 | C2 | semidirect |
| 9. #20298706 | C2 | semidirect |
| 10. #20298700 | C2 | semidirect |
| 11. C4×M16×C113 | C2 | semidirect |
| 110. C113 | #3183 | semidirect |
| 121. C4×M16 | D113 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20299132 | 2 |
| #20299000 | 2 |
| #20298982 | 2 |
| #20298953 | 2 |
| #20298856 | 2 |
| #20298851 | 2 |
| #20298844 | 2 |
| #20298711 | 2 |
| #20298706 | 2 |
| #20298700 | 2 |
| C4×M16×C113 | 2 |
| #3183 | 113 |