Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
228 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 228 conjugacy classes of subgroups — too many to draw. Only its 83 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 |
|---|---|---|
| 3. C3×C7×#107 | C2 | semidirect |
| 4. #10620657 | C2 | semidirect |
| 5. #10620647 | C2 | semidirect |
| 14. C8×D21 | C4 | semidirect |
| 17. C7×#107 | D3 | semidirect |
| 40. C3×#107 | D7 | semidirect |
| 77. #107 | D21 | semidirect |
| 97. C3×C7 | #427 | semidirect |
| 128. C7 | #4880 | semidirect |
| 142. C3 | #89652 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C8×D21 | 2 |
| #10621375 | 2 |
| C3×C7×#107 | 2 |
| #10620657 | 2 |
| #10620647 | 2 |
| #89652 | 3 |
| #4880 | 7 |