Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
412 conjugacy classes of subgroups; only the 171 normal subgroups are shown.
This group has 412 conjugacy classes of subgroups — too many to draw. Only its 171 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. #10621373 | C2 | semidirect |
| 5. #10621371 | C2 | semidirect |
| 25. C2×C3×C4×C7 | Q8 | semidirect |
| 57. C2×C4×C7 | Dic6 | semidirect |
| 92. C2×C3×C4 | Dic14 | semidirect |
| 98. C3×C7 | #544 | semidirect |
| 126. C2×C4 | Dic42 | semidirect |
| 129. C7 | #5500 | semidirect |
| 142. C3 | #90191 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×C7×C4⋊C4 | 2 |
| #10621409 | 2 |
| #10621407 | 2 |
| #10621373 | 2 |
| #10621371 | 2 |
| #90191 | 3 |
| #5500 | 7 |