Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
228 conjugacy classes of subgroups; only the 112 normal subgroups are shown.
This group has 228 conjugacy classes of subgroups — too many to draw. Only its 112 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. #10620523 | C2 | semidirect |
| 5. #10620520 | C2 | semidirect |
| 14. C2×C3×C7⋊C8 | C4 | semidirect |
| 39. C2×C7⋊C8 | Dic3 | semidirect |
| 100. C3×C7 | #427 | semidirect |
| 131. C7 | #5106 | semidirect |
| 143. C3 | #89770 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10621409 | 2 |
| C7×#926 | 2 |
| C22×C3×C7⋊C8 | 2 |
| #10620523 | 2 |
| #10620520 | 2 |
| #89770 | 3 |
| #5106 | 7 |