Finite Group DatabasebetaFinite Group DatabasebetaOrder 14464.
420 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 420 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. #20299252 | C2 | semidirect |
| 2. #20299251 | C2 | semidirect |
| 3. #20298950 | C2 | semidirect |
| 4. #20298935 | C2 | semidirect |
| 5. #20298845 | C2 | semidirect |
| 6. #20298804 | C2 | semidirect |
| 7. #20298744 | C2 | semidirect |
| 8. C4×#14268632 | C2 | semidirect |
| 9. #20298675 | C2 | semidirect |
| 10. #20298596 | C2 | semidirect |
| 11. #474×C113 | C2 | semidirect |
| 82. D4×C113 | #41 | semidirect |
| 133. C113 | #3330 | semidirect |
| 138. #474 | D113 | semidirect |
| 222. D4 | #14268648 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20299252 | 2 |
| #20299251 | 2 |
| #20298950 | 2 |
| #20298935 | 2 |
| #20298845 | 2 |
| #20298804 | 2 |
| #20298744 | 2 |
| C4×#14268632 | 2 |
| #20298675 | 2 |
| #20298596 | 2 |
| #474×C113 | 2 |
| #3330 | 113 |