Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
168 conjugacy classes of subgroups; only the 54 normal subgroups are shown.
This group has 168 conjugacy classes of subgroups — too many to draw. Only its 54 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. C4×C7×SL(2,𝔽3) | C2 | semidirect |
| 3. C7×#520 | C3 | semidirect |
| 4. C7×#41⋊C3 | C4 | semidirect |
| 12. #520⋊C3 | C7 | direct (N × H) |
| 15. C7×SL(2,𝔽3) | C2×C4 | semidirect |
| 17. C7×#41 | C3×C4 | semidirect |
| 28. C4×SL(2,𝔽3) | C2×C7 | semidirect |
| 32. #520 | C3×C7 | semidirect |
| 45. #41⋊C3 | C4×C7 | semidirect |
| 67. SL(2,𝔽3) | C2×C4×C7 | semidirect |
| 70. #41 | C3×C4×C7 | semidirect |
| 99. C7 | #520⋊C3 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C7×#41⋊C3 | 2 |
| C4×C7×SL(2,𝔽3) | 2 |
| C7×#520 | 3 |
| C3×C7×C4⋊C4 | 4 |
| #520⋊C3 | 7 |