Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
580 conjugacy classes of subgroups; only the 200 normal subgroups are shown.
This group has 580 conjugacy classes of subgroups — too many to draw. Only its 200 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. #10620890 | C2 | direct (N × H) |
| 44. C2×C7×Dic3 | Q8 | semidirect |
| 48. C2×C3×Dic7 | Q8 | semidirect |
| 84. C3×Dic7 | C2×Q8 | semidirect |
| 86. C7×Dic3 | C2×Q8 | semidirect |
| 100. C2×Dic7 | Dic6 | semidirect |
| 121. C2×C3×C7 | C4⋊Q8 | semidirect |
| 143. Dic7 | C2×Dic6 | semidirect |
| 156. C2×Dic3 | Dic14 | semidirect |
| 161. C3×C7 | C2×C4⋊Q8 | semidirect |
| 178. C2×C7 | #888 | semidirect |
| 192. Dic3 | C2×Dic14 | semidirect |
| 210. C7 | C2×#888 | semidirect |
| 211. C2×C3 | #6451 | semidirect |
| 226. C3 | C2×#6451 | semidirect |
| 227. C2 | #10620890 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×Dic42 | 2 |
| C22×#4248 | 2 |
| C2×C7×Dic3⋊C4 | 2 |
| C2×C3×Dic7⋊C4 | 2 |
| C2×Dic3⋊Dic7 | 2 |
| C2×Dic7⋊Dic3 | 2 |
| C2×Dic3×Dic7 | 2 |
| #10620890 | 2 |
| C2×#6451 | 3 |
| C2×#888 | 7 |