Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
228 conjugacy classes of subgroups; only the 126 normal subgroups are shown.
This group has 228 conjugacy classes of subgroups — too many to draw. Only its 126 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. C3×#6382 | C2 | semidirect |
| 5. C3×#6381 | C2 | semidirect |
| 6. #89770 | C3 | direct (N × H) |
| 14. C2×C3×C7⋊C8 | C4 | semidirect |
| 20. #6382 | C2×C3 | semidirect |
| 21. #6381 | C2×C3 | semidirect |
| 39. C2×C7⋊C8 | C3×C4 | semidirect |
| 100. C3×C7 | #427 | semidirect |
| 131. C7 | C3×#427 | semidirect |
| 143. C3 | #89770 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C7×#117 | 2 |
| C3×#6489 | 2 |
| C22×C3×C7⋊C8 | 2 |
| C3×#6382 | 2 |
| C3×#6381 | 2 |
| #89770 | 3 |
| C3×#427 | 7 |