Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
276 conjugacy classes of subgroups; only the 144 normal subgroups are shown.
This group has 276 conjugacy classes of subgroups — too many to draw. Only its 144 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 |
|---|---|---|
| 4. #10620518 | C2 | direct (N × H) |
| 26. C2×Dic21 | C8 | semidirect |
| 52. Dic21 | C2×C8 | semidirect |
| 74. C2×C3×C7 | C4⋊C8 | semidirect |
| 102. C3×C7 | C2×C4⋊C8 | semidirect |
| 112. C2×C7 | Dic3⋊C8 | semidirect |
| 136. C7 | C2×Dic3⋊C8 | semidirect |
| 137. C2×C3 | Dic7⋊C8 | semidirect |
| 150. C3 | C2×Dic7⋊C8 | semidirect |
| 151. C2 | #10620518 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×Dic21 | 2 |
| C22×C7×C3⋊C8 | 2 |
| C22×C3×C7⋊C8 | 2 |
| #10620518 | 2 |
| C2×Dic7⋊C8 | 3 |
| C2×Dic3⋊C8 | 7 |