Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
162 conjugacy classes of subgroups; only the 42 normal subgroups are shown.
This group has 162 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. C7×GU(2,𝔽3) | C2 | direct (N × H) |
| 4. C7×#41⋊C3 | C4 | semidirect |
| 6. C2×C7×SL(2,𝔽3) | C4 | semidirect |
| 13. C2×GU(2,𝔽3) | C7 | direct (N × H) |
| 15. C7×SL(2,𝔽3) | C2×C4 | semidirect |
| 31. GU(2,𝔽3) | C2×C7 | direct (N × H) |
| 51. #41⋊C3 | C4×C7 | semidirect |
| 53. C2×SL(2,𝔽3) | C4×C7 | semidirect |
| 72. SL(2,𝔽3) | C2×C4×C7 | semidirect |
| 90. C2×C7 | GU(2,𝔽3) | direct (N × H) |
| 110. C7 | C2×GU(2,𝔽3) | direct (N × H) |
| 125. C2 | C7×GU(2,𝔽3) | 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 |
| C7×GU(2,𝔽3) | 2 |
| C2×C7×#104 | 3 |
| C2×C7×C3⋊C8 | 4 |
| C2×GU(2,𝔽3) | 7 |