Finite Group DatabasebetaFinite Group DatabasebetaOrder 14464.
416 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 416 conjugacy classes of subgroups — too many to draw. Only its 149 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. #20298890 | C2 | semidirect |
| 3. #20298885 | C2 | semidirect |
| 4. #20298880 | C2 | semidirect |
| 5. #20298875 | C2 | semidirect |
| 6. #20298638 | C2 | semidirect |
| 7. #20298622 | C2 | semidirect |
| 9. C2×C4⋊Q8×C113 | C2 | semidirect |
| 36. #14268647 | Q8 | semidirect |
| 91. D452 | C2×Q8 | semidirect |
| 96. Dic226 | C2×Q8 | semidirect |
| 122. C113 | #3079 | semidirect |
| 123. C2×C4⋊Q8 | D113 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#14268647 | 2 |
| #20298890 | 2 |
| #20298885 | 2 |
| #20298880 | 2 |
| #20298875 | 2 |
| #20298638 | 2 |
| #20298622 | 2 |
| #20298597 | 2 |
| C2×C4⋊Q8×C113 | 2 |
| #3079 | 113 |