Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
280 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 280 conjugacy classes of subgroups — too many to draw. Only its 66 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×#66632 | C2 | semidirect |
| 2. C7×#940 | C2 | semidirect |
| 3. #10620990 | C2 | semidirect |
| 4. C2×#66562 | C2 | semidirect |
| 5. C3×#6406 | C2 | semidirect |
| 6. Dic3⋊(C7⋊C8) | C2 | semidirect |
| 7. #10620501 | C2 | semidirect |
| 27. #6406 | D3 | semidirect |
| 37. D84 | D4 | semidirect |
| 61. #940 | D7 | semidirect |
| 82. C7×Dic3 | D8 | semidirect |
| 161. C3×C7 | #459 | semidirect |
| 195. Dic3 | #1141 | semidirect |
| 214. C7 | #4786 | semidirect |
| 236. C3 | #89844 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#66632 | 2 |
| C7×#940 | 2 |
| #10620990 | 2 |
| C2×#66562 | 2 |
| C3×#6406 | 2 |
| Dic3⋊(C7⋊C8) | 2 |
| #10620501 | 2 |
| #89844 | 3 |
| #4786 | 7 |