Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
166 conjugacy classes of subgroups; only the 39 normal subgroups are shown.
This group has 166 conjugacy classes of subgroups — too many to draw. Only its 39 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×C8×A4 | C2 | semidirect |
| 3. A4×C7⋊C8 | C2 | semidirect |
| 4. C22×#1131 | C3 | semidirect |
| 10. C22×C7×C8 | C2×C3 | semidirect |
| 11. C22×C7⋊C8 | C2×C3 | semidirect |
| 37. #1131 | A4 | direct (N × H) |
| 40. C8×A4 | D7 | semidirect |
| 42. C7×A4 | M16 | semidirect |
| 61. C7×C8 | C2×A4 | semidirect |
| 63. C7⋊C8 | C2×A4 | semidirect |
| 76. C22×C8 | C3×D7 | semidirect |
| 79. C22×C7 | C3×M16 | semidirect |
| 118. A4 | #1131 | direct (N × H) |
| 138. C8 | A4×D7 | semidirect |
| 139. C7 | A4×M16 | semidirect |
| 150. C22 | C3×#1131 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×A4×D7 | 2 |
| C7×C8×A4 | 2 |
| A4×C7⋊C8 | 2 |
| C22×#1131 | 3 |
| C3×#1131 | 4 |
| A4×M16 | 7 |