Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
260 conjugacy classes of subgroups; only the 158 normal subgroups are shown.
This group has 260 conjugacy classes of subgroups — too many to draw. Only its 158 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 |
|---|---|---|
| 4. C7×#808 | C2 | direct (N × H) |
| 13. C2×C7×C3⋊C8 | C4 | semidirect |
| 19. C2×#808 | C7 | direct (N × H) |
| 29. C7×C3⋊C8 | C2×C4 | semidirect |
| 42. #808 | C2×C7 | direct (N × H) |
| 70. C2×C3⋊C8 | C4×C7 | semidirect |
| 72. C2×C3×C7 | #106 | semidirect |
| 98. C3⋊C8 | C2×C4×C7 | semidirect |
| 99. C3×C7 | C2×#106 | semidirect |
| 109. C2×C7 | #808 | direct (N × H) |
| 132. C7 | C2×#808 | direct (N × H) |
| 133. C2×C3 | C7×#106 | semidirect |
| 146. C3 | C2×C7×#106 | semidirect |
| 147. C2 | C7×#808 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×C7×C4⋊C4 | 2 |
| C2×C7×C4⋊Dic3 | 2 |
| C22×C7×C3⋊C8 | 2 |
| C7×#808 | 2 |
| C2×C7×#106 | 3 |
| C2×#808 | 7 |