Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
224 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 224 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. C4×Dic42 | C2 | semidirect |
| 5. C3×C7×C4⋊C8 | C2 | semidirect |
| 7. #10620655 | C2 | semidirect |
| 26. C7×C4⋊C8 | D3 | semidirect |
| 62. C3×C4⋊C8 | D7 | semidirect |
| 113. C4⋊C8 | D21 | semidirect |
| 142. C3×C7 | #464 | semidirect |
| 186. C7 | #4845 | semidirect |
| 202. C3 | #89617 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Dic84 | 2 |
| C2×#66623 | 2 |
| #10621358 | 2 |
| C4×Dic42 | 2 |
| C3×C7×C4⋊C8 | 2 |
| #10620660 | 2 |
| #10620655 | 2 |
| #89617 | 3 |
| #4845 | 7 |