Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
166 conjugacy classes of subgroups; only the 45 normal subgroups are shown.
This group has 166 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 |
|---|---|---|
| 2. A4×C7⋊C8 | C2 | semidirect |
| 3. C22×#1136 | C3 | semidirect |
| 12. C22×C7⋊C8 | C2×C3 | semidirect |
| 28. #1136 | A4 | direct (N × H) |
| 34. C7×A4 | M16 | semidirect |
| 53. C7⋊C8 | C2×A4 | semidirect |
| 72. C22×C7 | C3×M16 | semidirect |
| 102. A4 | #1136 | direct (N × H) |
| 121. C7 | A4×M16 | semidirect |
| 131. C22 | C3×#1136 | 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 |
| A4×C7⋊C8 | 2 |
| C22×#1136 | 3 |
| C3×#1136 | 4 |
| A4×M16 | 7 |