Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
244 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 244 conjugacy classes of subgroups — too many to draw. Only its 78 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 |
|---|---|---|
| 2. Dic6×Dic7 | C2 | semidirect |
| 4. #10620647 | C2 | semidirect |
| 5. C7×#810 | C2 | semidirect |
| 7. C3⋊C8×Dic7 | C2 | semidirect |
| 20. #66563 | C4 | semidirect |
| 35. C7×Dic6 | C2×C4 | semidirect |
| 41. C3⋊(C7⋊C8) | C2×C4 | semidirect |
| 59. #810 | D7 | semidirect |
| 71. C3×Dic7 | SD16 | semidirect |
| 121. Dic7 | #214 | semidirect |
| 133. Dic6 | C4×D7 | semidirect |
| 136. C3×C7 | C4×SD16 | semidirect |
| 178. C7 | C4×#214 | semidirect |
| 194. C3 | #89560 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#6456 | 2 |
| Dic6×Dic7 | 2 |
| C2×#66563 | 2 |
| #10620647 | 2 |
| C7×#810 | 2 |
| #10620500 | 2 |
| C3⋊C8×Dic7 | 2 |
| #89560 | 3 |
| C4×#214 | 7 |