Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
580 conjugacy classes of subgroups; only the 208 normal subgroups are shown.
This group has 580 conjugacy classes of subgroups — too many to draw. Only its 208 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 |
|---|---|---|
| 6. #10621032 | C2 | direct (N × H) |
| 27. C2×C3×C4×C7 | Q8 | semidirect |
| 30. C2×Dic21 | Q8 | semidirect |
| 59. C3×C4×C7 | C2×Q8 | semidirect |
| 61. Dic21 | C2×Q8 | semidirect |
| 68. C2×C4×C7 | Dic6 | semidirect |
| 88. C2×C3×C7 | C4⋊Q8 | semidirect |
| 103. C4×C7 | C2×Dic6 | semidirect |
| 110. C2×C3×C4 | Dic14 | semidirect |
| 119. C3×C7 | C2×C4⋊Q8 | semidirect |
| 131. C2×C7 | #888 | semidirect |
| 140. C3×C4 | C2×Dic14 | semidirect |
| 154. C2×C4 | #4248 | semidirect |
| 156. C7 | C2×#888 | semidirect |
| 157. C2×C3 | #6451 | semidirect |
| 169. C4 | C2×#4248 | semidirect |
| 170. C3 | C2×#6451 | semidirect |
| 171. C2 | #10621032 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#4248 | 2 |
| C2×C4×Dic21 | 2 |
| C2×C7×C4⋊Dic3 | 2 |
| C2×C3×C4⋊Dic7 | 2 |
| C2×#66577 | 2 |
| #10621032 | 2 |
| C2×#6451 | 3 |
| C2×#888 | 7 |