Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
338 conjugacy classes of subgroups; only the 49 normal subgroups are shown.
This group has 338 conjugacy classes of subgroups — too many to draw. Only its 49 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×Dic7⋊A4 | C2 | semidirect |
| 3. C22×C22⋊Dic7 | C3 | semidirect |
| 5. C22×C22⋊ΓL(1,𝔽8) | C4 | semidirect |
| 10. C23×Dic7 | C2×C3 | semidirect |
| 25. C24×C7 | C3×C4 | semidirect |
| 34. C22⋊Dic7 | A4 | semidirect |
| 37. C22⋊ΓL(1,𝔽8) | C22⋊C4 | semidirect |
| 67. C2×Dic7 | C2×A4 | semidirect |
| 97. C22×C7 | C3×C22⋊C4 | semidirect |
| 98. C22×C7 | C4×A4 | semidirect |
| 113. C24 | ΓL(1,𝔽8)⋊C4 | semidirect |
| 160. C7 | A4×C22⋊C4 | semidirect |
| 180. C22 | (C22⋊Dic7)⋊C3 | semidirect |
| 181. C22 | Dic7⋊A4 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C22⋊ΓL(1,𝔽8) | 2 |
| C2×Dic7⋊A4 | 2 |
| C22×C22⋊Dic7 | 3 |
| (C22⋊Dic7)⋊C3 | 4 |
| A4×C22⋊C4 | 7 |