Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
308 conjugacy classes of subgroups; only the 158 normal subgroups are shown.
This group has 308 conjugacy classes of subgroups — too many to draw. Only its 158 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 |
|---|---|---|
| 5. #89749 | C3 | direct (N × H) |
| 12. C3×C4×Dic7 | C4 | semidirect |
| 35. C4×Dic7 | C3×C4 | semidirect |
| 97. C3×C7 | #382 | semidirect |
| 130. C7 | C3×#382 | semidirect |
| 145. C3 | #89749 | direct (N × H) |
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 |
| C2×C3×C4⋊Dic7 | 2 |
| C2×C3×C4×Dic7 | 2 |
| C3×C7⋊#95 | 2 |
| #89749 | 3 |
| C3×#382 | 7 |