Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
244 conjugacy classes of subgroups; only the 102 normal subgroups are shown.
This group has 244 conjugacy classes of subgroups — too many to draw. Only its 102 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 |
|---|---|---|
| 3. C3×#6450 | C2 | semidirect |
| 5. C3×#6390 | C2 | semidirect |
| 6. C3×C8×Dic7 | C2 | semidirect |
| 7. C3×#6382 | C2 | semidirect |
| 8. #89530 | C3 | direct (N × H) |
| 15. C3×#1142 | C4 | semidirect |
| 23. #6450 | C2×C3 | semidirect |
| 25. #6390 | C2×C3 | semidirect |
| 26. C8×Dic7 | C2×C3 | semidirect |
| 27. #6382 | C2×C3 | semidirect |
| 40. C3×Dic14 | C2×C4 | semidirect |
| 42. C3×C7⋊C8 | C2×C4 | semidirect |
| 49. #1142 | C3×C4 | semidirect |
| 72. C3×Dic7 | SD16 | semidirect |
| 85. Dic14 | C2×C3×C4 | semidirect |
| 87. C7⋊C8 | C2×C3×C4 | semidirect |
| 121. Dic7 | C3×SD16 | semidirect |
| 136. C3×C7 | C4×SD16 | semidirect |
| 178. C7 | C3×C4×SD16 | semidirect |
| 194. C3 | #89530 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×D4×Dic7 | 2 |
| C2×C3×#1142 | 2 |
| C3×#6450 | 2 |
| C3×C7×#102 | 2 |
| C3×#6390 | 2 |
| C3×C8×Dic7 | 2 |
| C3×#6382 | 2 |
| #89530 | 3 |
| C3×C4×SD16 | 7 |