Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
372 conjugacy classes of subgroups; only the 182 normal subgroups are shown.
This group has 372 conjugacy classes of subgroups — too many to draw. Only its 182 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 |
|---|---|---|
| 8. C2×C3×C7×Q8 | C4 | semidirect |
| 19. #5229 | C7 | direct (N × H) |
| 32. C2×C7×Dic3 | Q8 | semidirect |
| 35. C2×C7×Q8 | Dic3 | semidirect |
| 71. C2×C3×Q8 | C4×C7 | semidirect |
| 108. C2×Dic3 | C7×Q8 | semidirect |
| 109. C3×C7 | #391 | semidirect |
| 112. C2×Q8 | C7×Dic3 | semidirect |
| 146. C7 | #5229 | direct (N × H) |
| 161. C3 | C7×#391 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C3×C7×Q8 | 2 |
| C2×C7×C4⋊Dic3 | 2 |
| C2×C4×C7×Dic3 | 2 |
| C7×C3⋊#95 | 2 |
| C7×#391 | 3 |
| #5229 | 7 |