Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
162 conjugacy classes of subgroups; only the 42 normal subgroups are shown.
This group has 162 conjugacy classes of subgroups — too many to draw. Only its 42 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. C7×A4⋊C8 | C2 | semidirect |
| 13. #5409 | C7 | direct (N × H) |
| 32. A4⋊C8 | C2×C7 | semidirect |
| 34. C7×A4 | M16 | semidirect |
| 72. C22×C7 | #208 | semidirect |
| 102. A4 | C7×M16 | semidirect |
| 121. C7 | #5409 | direct (N × H) |
| 131. C22 | C7×#208 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×C7×A4 | 2 |
| C7×A4⋊C8 | 2 |
| C7×#407 | 3 |
| C7×#208 | 4 |
| #5409 | 7 |