Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
284 conjugacy classes of subgroups; only the 190 normal subgroups are shown.
This group has 284 conjugacy classes of subgroups — too many to draw. Only its 190 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 |
|---|---|---|
| 3. C7×#803 | C2 | semidirect |
| 4. C4×C7×C3⋊C8 | C2 | semidirect |
| 11. C7×#208 | C4 | direct (N × H) |
| 17. C4×#208 | C7 | direct (N × H) |
| 25. C7×C3⋊C8 | C2×C4 | semidirect |
| 35. #803 | C2×C7 | semidirect |
| 36. C4×C3⋊C8 | C2×C7 | semidirect |
| 42. C3×C4×C7 | M16 | semidirect |
| 58. #208 | C4×C7 | direct (N × H) |
| 71. C4×C7 | #208 | direct (N × H) |
| 81. C3⋊C8 | C2×C4×C7 | semidirect |
| 82. C3×C7 | C4×M16 | semidirect |
| 98. C3×C4 | C7×M16 | semidirect |
| 108. C7 | C4×#208 | direct (N × H) |
| 116. C4 | C7×#208 | direct (N × H) |
| 119. C3 | C4×C7×M16 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×C42×C7 | 2 |
| C2×C7×#208 | 2 |
| C7×#803 | 2 |
| C4×C7×C3⋊C8 | 2 |
| C4×C7×M16 | 3 |
| C4×#208 | 7 |