Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
172 conjugacy classes of subgroups; only the 39 normal subgroups are shown.
This group has 172 conjugacy classes of subgroups — too many to draw. Only its 39 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. C4×C7×SL(2,𝔽3) | C2 | semidirect |
| 3. SL(2,𝔽3)×Dic7 | C2 | semidirect |
| 4. #90263 | C3 | semidirect |
| 6. D7×SL(2,𝔽3) | C4 | semidirect |
| 9. C4×C7×Q8 | C2×C3 | semidirect |
| 10. Q8×Dic7 | C2×C3 | semidirect |
| 22. Q8×D7 | C3×C4 | semidirect |
| 36. C4×SL(2,𝔽3) | D7 | semidirect |
| 68. C4×Q8 | C3×D7 | semidirect |
| 124. C7 | #519⋊C3 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D7×SL(2,𝔽3) | 2 |
| C4×C7×SL(2,𝔽3) | 2 |
| SL(2,𝔽3)×Dic7 | 2 |
| #90263 | 3 |
| C3×(C2×D7)⋊C4 | 4 |
| #519⋊C3 | 7 |