Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
168 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 168 conjugacy classes of subgroups — too many to draw. Only its 72 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 |
|---|---|---|
| 2. C7×#812 | C2 | semidirect |
| 3. C2×C3×C7⋊C16 | C2 | semidirect |
| 4. #10620471 | C2 | semidirect |
| 5. D21⋊C16 | C2 | semidirect |
| 17. C2×C7⋊C16 | D3 | semidirect |
| 39. #812 | D7 | semidirect |
| 85. C3×C7 | #504 | semidirect |
| 110. C7 | #4901 | semidirect |
| 119. C3 | #89679 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10621384 | 2 |
| C7×#812 | 2 |
| C2×C3×C7⋊C16 | 2 |
| #10620471 | 2 |
| D21⋊C16 | 2 |
| #89679 | 3 |
| #4901 | 7 |