Finite Group DatabasebetaFinite Group DatabasebetaOrder 14464.
342 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 342 conjugacy classes of subgroups — too many to draw. Only its 115 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. #20299000 | C2 | semidirect |
| 3. #20298937 | C2 | semidirect |
| 4. #20298927 | C2 | semidirect |
| 5. #20298905 | C2 | semidirect |
| 6. #20298836 | C2 | semidirect |
| 7. #20298836 | C2 | semidirect |
| 9. #20298635 | C2 | semidirect |
| 10. #107×D113 | C2 | semidirect |
| 11. C4×Q16×C113 | C2 | semidirect |
| 115. C113 | #3336 | semidirect |
| 123. C4×Q16 | D113 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20299289 | 2 |
| #20299000 | 2 |
| #20298937 | 2 |
| #20298927 | 2 |
| #20298905 | 2 |
| #20298836 | 2 |
| C8×D452 | 2 |
| #20298635 | 2 |
| #107×D113 | 2 |
| C4×Q16×C113 | 2 |
| #3336 | 113 |