Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
172 conjugacy classes of subgroups; only the 36 normal subgroups are shown.
This group has 172 conjugacy classes of subgroups — too many to draw. Only its 36 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×#834 | C2 | semidirect |
| 3. C3×#6408 | C2 | semidirect |
| 8. C2×D84 | C4 | semidirect |
| 9. C4×Dic21 | C4 | semidirect |
| 14. #6408 | D3 | semidirect |
| 36. #834 | D7 | semidirect |
| 99. C3×C7 | #353 | semidirect |
| 135. C7 | #4474 | semidirect |
| 153. C3 | #89269 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10621423 | 2 |
| C7×#834 | 2 |
| C3×#6408 | 2 |
| #89269 | 3 |
| #4474 | 7 |