Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
188 conjugacy classes of subgroups; only the 42 normal subgroups are shown.
This group has 188 conjugacy classes of subgroups — too many to draw. Only its 42 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. C3×C7×#99 | C2 | semidirect |
| 3. C3×#6407 | C2 | semidirect |
| 4. #89266 | C3 | direct (N × H) |
| 5. C23×C3×D7 | C4 | semidirect |
| 9. C3×C22⋊Dic7 | C4 | semidirect |
| 13. C7×#99 | C2×C3 | semidirect |
| 14. #6407 | C2×C3 | semidirect |
| 27. C23×D7 | C3×C4 | semidirect |
| 31. C22⋊Dic7 | C3×C4 | semidirect |
| 36. C3×#99 | D7 | semidirect |
| 76. #99 | C3×D7 | semidirect |
| 101. C3×C7 | AΣL(1,𝔽16) | semidirect |
| 138. C7 | C3×AΣL(1,𝔽16) | semidirect |
| 157. C3 | #89266 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#6500 | 2 |
| C3×C7×#99 | 2 |
| C3×#6407 | 2 |
| #89266 | 3 |
| C3×AΣL(1,𝔽16) | 7 |