Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
130 conjugacy classes of subgroups; only the 35 normal subgroups are shown.
This group has 130 conjugacy classes of subgroups — too many to draw. Only its 35 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 |
|---|---|---|
| 4. #90260 | C3 | semidirect |
| 18. C7×SL(2,𝔽3) | Q8 | semidirect |
| 73. SL(2,𝔽3) | Dic14 | semidirect |
| 104. C7 | #557⋊C3 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×C7×SL(2,𝔽3) | 2 |
| SL(2,𝔽3)×Dic7 | 2 |
| #90260 | 3 |
| C3×Dic7⋊C4 | 4 |
| #557⋊C3 | 7 |