Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
154 conjugacy classes of subgroups; only the 45 normal subgroups are shown.
This group has 154 conjugacy classes of subgroups — too many to draw. Only its 45 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 |
|---|---|---|
| 3. Q8×Dic14 | C3 | semidirect |
| 15. C7×SL(2,𝔽3) | Q8 | semidirect |
| 32. C7×Q8 | C3×Q8 | semidirect |
| 39. Dic14 | SL(2,𝔽3) | direct (N × H) |
| 60. SL(2,𝔽3) | Dic14 | direct (N × H) |
| 80. Q8 | C3×Dic14 | semidirect |
| 86. C7 | Q8×SL(2,𝔽3) | 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 |
| Q8×Dic14 | 3 |
| C2×C3×Dic14 | 4 |
| Q8×SL(2,𝔽3) | 7 |