Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
372 conjugacy classes of subgroups; only the 106 normal subgroups are shown.
This group has 372 conjugacy classes of subgroups — too many to draw. Only its 106 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. C2×C7×Dic3⋊C4 | C2 | semidirect |
| 3. C2×C3×C4⋊Dic7 | C2 | semidirect |
| 4. C2×Dic7⋊Dic3 | C2 | semidirect |
| 7. #10620529 | C2 | semidirect |
| 26. C2×C4⋊Dic7 | D3 | semidirect |
| 74. C2×Dic3⋊C4 | D7 | semidirect |
| 197. C3×C7 | #396 | semidirect |
| 265. C7 | #4994 | semidirect |
| 294. C3 | #89766 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#66631 | 2 |
| C2×C7×Dic3⋊C4 | 2 |
| C2×C3×C4⋊Dic7 | 2 |
| C2×Dic7⋊Dic3 | 2 |
| C2×#66575 | 2 |
| #10620529 | 2 |
| #89766 | 3 |
| #4994 | 7 |