Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
128 conjugacy classes of subgroups; only the 37 normal subgroups are shown.
This group has 128 conjugacy classes of subgroups — too many to draw. Only its 37 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. C3×C7×#101 | C2 | semidirect |
| 3. #10620675 | C2 | semidirect |
| 13. C7×#101 | D3 | semidirect |
| 33. C3×#101 | D7 | semidirect |
| 64. #101 | D21 | semidirect |
| 81. C3×C7 | #355 | semidirect |
| 108. C7 | #4477 | semidirect |
| 119. C3 | #89272 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10621430 | 2 |
| C3×C7×#101 | 2 |
| #10620675 | 2 |
| #89272 | 3 |
| #4477 | 7 |