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 |
|---|---|---|
| 1. C2×#16813622 | C2 | semidirect |
| 3. #20298992 | C2 | semidirect |
| 4. #20298967 | C2 | semidirect |
| 5. #20298809 | C2 | semidirect |
| 6. #20298804 | C2 | semidirect |
| 7. #20298756 | C2 | semidirect |
| 9. #432×C113 | C2 | semidirect |
| 116. C113 | #3218 | semidirect |
| 125. #432 | D113 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16813622 | 2 |
| #20299132 | 2 |
| #20298992 | 2 |
| #20298967 | 2 |
| #20298809 | 2 |
| #20298804 | 2 |
| #20298756 | 2 |
| #20298739 | 2 |
| #432×C113 | 2 |
| #3218 | 113 |