Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
220 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 220 conjugacy classes of subgroups — too many to draw. Only its 69 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 |
|---|---|---|
| 1. C2×Dic84 | C2 | semidirect |
| 4. C3×C7×#106 | C2 | semidirect |
| 5. #10620649 | C2 | semidirect |
| 19. C7×#106 | D3 | semidirect |
| 45. C3×#106 | D7 | semidirect |
| 82. #106 | D21 | semidirect |
| 103. C3×C7 | #470 | semidirect |
| 135. C7 | #4867 | semidirect |
| 147. C3 | #89640 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Dic84 | 2 |
| C2×#66622 | 2 |
| #10621380 | 2 |
| C3×C7×#106 | 2 |
| #10620649 | 2 |
| #89640 | 3 |
| #4867 | 7 |