Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
660 conjugacy classes of subgroups; only the 243 normal subgroups are shown.
This group has 660 conjugacy classes of subgroups — too many to draw. Only its 243 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 |
|---|---|---|
| 4. C2×#66629 | C2 | semidirect |
| 5. C2×C4×Dic21 | C2 | semidirect |
| 6. #10621360 | C2 | direct (N × H) |
| 10. C22×Dic21 | C4 | semidirect |
| 17. #66629 | C22 | semidirect |
| 18. C4×Dic21 | C22 | semidirect |
| 35. C2×Dic21 | C2×C4 | semidirect |
| 92. C2×C3×C7 | #117 | semidirect |
| 124. C3×C7 | C2×#117 | semidirect |
| 137. C2×C7 | #877 | semidirect |
| 163. C7 | C2×#877 | semidirect |
| 165. C2×C3 | #6440 | semidirect |
| 178. C3 | C2×#6440 | semidirect |
| 180. C2 | #10621360 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×Dic21 | 2 |
| C2×C3×C7×C22⋊C4 | 2 |
| C2×#66636 | 2 |
| C2×#66629 | 2 |
| C2×C4×Dic21 | 2 |
| #10621360 | 2 |
| C2×#6440 | 3 |
| C2×#877 | 7 |