Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
120 conjugacy classes of subgroups; only the 37 normal subgroups are shown.
This group has 120 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 |
|---|---|---|
| 78. C3×C7 | #356 | semidirect |
| 103. C7 | #4478 | semidirect |
| 112. C3 | #89273 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10621427 | 2 |
| C3×C7×#101 | 2 |
| #10620675 | 2 |
| #89273 | 3 |
| #4478 | 7 |