Finite Group DatabasebetaFinite Group DatabasebetaOrder 14464.
416 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 416 conjugacy classes of subgroups — too many to draw. Only its 133 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. C4⋊Q8×D113 | C2 | semidirect |
| 3. #20298894 | C2 | semidirect |
| 4. #20298890 | C2 | semidirect |
| 5. #20298888 | C2 | semidirect |
| 6. #20298882 | C2 | semidirect |
| 7. #20298876 | C2 | semidirect |
| 8. #20298637 | C2 | semidirect |
| 9. #20298620 | C2 | semidirect |
| 11. #476×C113 | C2 | semidirect |
| 44. #14268646 | Q8 | semidirect |
| 86. D4×C113 | C2×Q8 | semidirect |
| 110. Dic226 | C2×Q8 | semidirect |
| 138. C113 | #3079 | semidirect |
| 144. #476 | D113 | semidirect |
| 229. D4 | Q8×D113 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4⋊Q8×D113 | 2 |
| C4×#14268646 | 2 |
| #20298894 | 2 |
| #20298890 | 2 |
| #20298888 | 2 |
| #20298882 | 2 |
| #20298876 | 2 |
| #20298637 | 2 |
| #20298620 | 2 |
| #20298596 | 2 |
| #476×C113 | 2 |
| #3079 | 113 |