Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
346 conjugacy classes of subgroups; only the 54 normal subgroups are shown.
This group has 346 conjugacy classes of subgroups — too many to draw. Only its 54 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×C7×SL(2,ℤ/4) | C2 | semidirect |
| 5. C22×C7×A4 | C4 | semidirect |
| 14. #5432 | C7 | direct (N × H) |
| 25. C24×C7 | Dic3 | semidirect |
| 36. C2×SL(2,ℤ/4) | C2×C7 | semidirect |
| 40. C7×A4 | C22⋊C4 | semidirect |
| 69. C22×A4 | C4×C7 | semidirect |
| 97. C22×C7 | #217 | semidirect |
| 98. C22×C7 | SL(2,ℤ/4) | semidirect |
| 113. C24 | C7×Dic3 | semidirect |
| 133. A4 | C7×C22⋊C4 | semidirect |
| 160. C7 | #5432 | direct (N × H) |
| 180. C22 | C7×#217 | semidirect |
| 181. C22 | C7×SL(2,ℤ/4) | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C7×A4 | 2 |
| C2×C7×SL(2,ℤ/4) | 2 |
| C7×#379 | 3 |
| C7×#217 | 4 |
| #5432 | 7 |