Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
280 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 280 conjugacy classes of subgroups — too many to draw. Only its 77 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×D168 | C2 | semidirect |
| 2. #10621357 | C2 | semidirect |
| 3. C4×D84 | C2 | semidirect |
| 4. C3×C7×C4⋊C8 | C2 | semidirect |
| 5. #10620660 | C2 | semidirect |
| 20. C7×C4⋊C8 | D3 | semidirect |
| 34. D84 | D4 | semidirect |
| 50. C3×C4⋊C8 | D7 | semidirect |
| 60. C3×C4×C7 | D8 | semidirect |
| 97. C4⋊C8 | D21 | semidirect |
| 107. C4×C7 | D24 | semidirect |
| 125. C3×C7 | #459 | semidirect |
| 149. C3×C4 | D56 | semidirect |
| 167. C7 | #4843 | semidirect |
| 182. C4 | D168 | semidirect |
| 185. C3 | #89615 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D168 | 2 |
| #10621357 | 2 |
| C4×D84 | 2 |
| C3×C7×C4⋊C8 | 2 |
| #10620660 | 2 |
| #89615 | 3 |
| #4843 | 7 |