Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
192 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 192 conjugacy classes of subgroups — too many to draw. Only its 77 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 |
|---|---|---|
| 30. Dic42 | Q8 | semidirect |
| 100. C3×C7 | #477 | semidirect |
| 131. C7 | #5091 | semidirect |
| 143. C3 | #89863 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C7×C4⋊Q8 | 2 |
| C4×Dic42 | 2 |
| #10620649 | 2 |
| #10620646 | 2 |
| C4⋊(C3⋊(C7⋊C8)) | 2 |
| #89863 | 3 |
| #5091 | 7 |