Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
364 conjugacy classes of subgroups; only the 138 normal subgroups are shown.
This group has 364 conjugacy classes of subgroups — too many to draw. Only its 138 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 |
|---|---|---|
| 21. #4656 | C7 | direct (N × H) |
| 27. C2×C3×C4×C7 | Q8 | semidirect |
| 35. C2×C7×Dic3 | Q8 | semidirect |
| 75. C2×C4×C7 | Dic6 | semidirect |
| 111. C2×C3×C4 | C7×Q8 | semidirect |
| 119. C2×Dic3 | C7×Q8 | semidirect |
| 121. C3×C7 | #395 | semidirect |
| 159. C2×C4 | C7×Dic6 | semidirect |
| 161. C7 | #4656 | direct (N × H) |
| 177. C3 | C7×#395 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C7×Dic6 | 2 |
| C2×C7×C4⋊Dic3 | 2 |
| C2×C7×Dic3⋊C4 | 2 |
| C3×C7×#95 | 2 |
| C7×C3⋊#95 | 2 |
| C7×#395 | 3 |
| #4656 | 7 |