Finite Group DatabasebetaFinite Group DatabasebetaOrder 14464.
396 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 396 conjugacy classes of subgroups — too many to draw. Only its 117 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. #20299305 | C2 | semidirect |
| 2. #20299268 | C2 | semidirect |
| 3. #20298961 | C2 | semidirect |
| 4. #20298944 | C2 | semidirect |
| 5. #20298900 | C2 | semidirect |
| 6. #20298889 | C2 | semidirect |
| 7. #20298791 | C2 | semidirect |
| 8. #20298725 | C2 | semidirect |
| 9. #20298710 | C2 | semidirect |
| 10. C4×#14268632 | C2 | semidirect |
| 11. #459×C113 | C2 | semidirect |
| 82. D4×C113 | #41 | semidirect |
| 130. C113 | #3366 | semidirect |
| 138. #459 | D113 | semidirect |
| 218. D4 | #14268646 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20299305 | 2 |
| #20299268 | 2 |
| #20298961 | 2 |
| #20298944 | 2 |
| #20298900 | 2 |
| #20298889 | 2 |
| #20298791 | 2 |
| #20298725 | 2 |
| #20298710 | 2 |
| C4×#14268632 | 2 |
| #459×C113 | 2 |
| #3366 | 113 |