Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
144 conjugacy classes of subgroups; only the 38 normal subgroups are shown.
This group has 144 conjugacy classes of subgroups — too many to draw. Only its 38 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 | semidirect |
| 4. C7×#41⋊C3 | C4 | semidirect |
| 6. C2×C7×SL(2,𝔽3) | C4 | semidirect |
| 13. #5423 | C7 | direct (N × H) |
| 31. GU(2,𝔽3) | C2×C7 | semidirect |
| 50. #41⋊C3 | C4×C7 | semidirect |
| 52. C2×SL(2,𝔽3) | C4×C7 | semidirect |
| 108. C7 | #5423 | 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 |
| C7×#421 | 3 |
| C7×#208 | 4 |
| #5423 | 7 |