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×#859 | C2 | semidirect |
| 4. C2×C7×SL(2,𝔽3) | C4 | semidirect |
| 12. #5420 | C7 | direct (N × H) |
| 18. C2×C7×Q8 | Dic3 | semidirect |
| 27. #859 | C2×C7 | semidirect |
| 44. C2×SL(2,𝔽3) | C4×C7 | semidirect |
| 68. C2×Q8 | C7×Dic3 | semidirect |
| 94. C7 | #5420 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C7×SL(2,𝔽3) | 2 |
| C7×#859 | 2 |
| C7×#419 | 3 |
| C7×#217 | 4 |
| #5420 | 7 |