Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
160 conjugacy classes of subgroups; only the 34 normal subgroups are shown.
This group has 160 conjugacy classes of subgroups — too many to draw. Only its 34 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. C2×C7×#226 | C2 | semidirect |
| 3. C7×#859 | C2 | semidirect |
| 16. #5419 | C7 | direct (N × H) |
| 36. C2×#226 | C2×C7 | semidirect |
| 37. #859 | C2×C7 | semidirect |
| 77. C22×C7 | #226 | semidirect |
| 128. C7 | #5419 | direct (N × H) |
| 135. C22 | C7×#226 | semidirect |
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 |
| C2×C7×#226 | 2 |
| C7×#859 | 2 |
| C7×#451 | 3 |
| C7×#217 | 4 |
| #5419 | 7 |