Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
134 conjugacy classes of subgroups; only the 34 normal subgroups are shown.
This group has 134 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 |
|---|---|---|
| 6. C7×#226 | C4 | semidirect |
| 15. #5388 | C7 | direct (N × H) |
| 51. #226 | C4×C7 | semidirect |
| 104. C7 | #5388 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C7×#226 | 2 |
| C4×C7×SL(2,𝔽3) | 2 |
| C7×#859 | 2 |
| C7×#441 | 3 |
| C7×Dic3⋊C4 | 4 |
| #5388 | 7 |