Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
240 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 240 conjugacy classes of subgroups — too many to draw. Only its 74 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 |
|---|---|---|
| 1. C7×#887 | C2 | semidirect |
| 5. C3×#6381 | C2 | semidirect |
| 6. #10620507 | C2 | semidirect |
| 7. #10620488 | C2 | semidirect |
| 20. #66568 | C4 | semidirect |
| 26. #6381 | D3 | semidirect |
| 38. C7×Dic6 | C2×C4 | semidirect |
| 42. C3×C7⋊C8 | C2×C4 | semidirect |
| 57. #887 | D7 | semidirect |
| 87. C7⋊C8 | C4×D3 | semidirect |
| 133. Dic6 | C4×D7 | semidirect |
| 136. C3×C7 | #440 | semidirect |
| 178. C7 | #4889 | semidirect |
| 194. C3 | #89798 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#887 | 2 |
| #10620990 | 2 |
| C2×#66568 | 2 |
| #10620648 | 2 |
| C3×#6381 | 2 |
| #10620507 | 2 |
| #10620488 | 2 |
| #89798 | 3 |
| #4889 | 7 |