Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
580 conjugacy classes of subgroups; only the 224 normal subgroups are shown.
This group has 580 conjugacy classes of subgroups — too many to draw. Only its 224 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 |
|---|---|---|
| 5. #10620951 | C2 | direct (N × H) |
| 29. C2×C7×Dic3 | Q8 | semidirect |
| 55. C7×Dic3 | C2×Q8 | semidirect |
| 78. C2×C3×C7 | C4⋊Q8 | semidirect |
| 101. C2×Dic3 | Dic14 | semidirect |
| 104. C3×C7 | C2×C4⋊Q8 | semidirect |
| 115. C2×C7 | #944 | semidirect |
| 124. Dic3 | C2×Dic14 | semidirect |
| 136. C7 | C2×#944 | semidirect |
| 137. C2×C3 | #6432 | semidirect |
| 147. C3 | C2×#6432 | semidirect |
| 148. C2 | #10620951 | 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×C3×Dic14 | 2 |
| C2×C4×C7×Dic3 | 2 |
| C2×Dic3⋊Dic7 | 2 |
| #10620951 | 2 |
| C2×#6432 | 3 |
| C2×#944 | 7 |