Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
444 conjugacy classes of subgroups; only the 187 normal subgroups are shown.
This group has 444 conjugacy classes of subgroups — too many to draw. Only its 187 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. #10621353 | C2 | semidirect |
| 5. #10621352 | C2 | semidirect |
| 6. C4×Dic42 | C2 | semidirect |
| 28. C2×C3×C4×C7 | Q8 | semidirect |
| 63. C2×C4×C7 | Dic6 | semidirect |
| 100. C2×C3×C4 | Dic14 | semidirect |
| 107. C3×C7 | #533 | semidirect |
| 134. C2×C4 | Dic42 | semidirect |
| 139. C7 | #5470 | semidirect |
| 151. C3 | #90161 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×C42×C7 | 2 |
| #10621409 | 2 |
| #10621407 | 2 |
| #10621353 | 2 |
| #10621352 | 2 |
| C4×Dic42 | 2 |
| #90161 | 3 |
| #5470 | 7 |