Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
240 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 240 conjugacy classes of subgroups — too many to draw. Only its 82 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. #10620893 | C2 | semidirect |
| 5. #10620523 | C2 | semidirect |
| 6. #10620506 | C2 | semidirect |
| 7. #10620489 | C2 | semidirect |
| 17. C3×#1142 | C4 | semidirect |
| 40. C3×Dic14 | C2×C4 | semidirect |
| 41. C3×C7⋊C8 | C2×C4 | semidirect |
| 49. #1142 | Dic3 | semidirect |
| 85. Dic14 | C2×Dic3 | semidirect |
| 87. C7⋊C8 | C2×Dic3 | semidirect |
| 136. C3×C7 | #440 | semidirect |
| 178. C7 | #5164 | semidirect |
| 194. C3 | #89529 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D4×Dic21 | 2 |
| C2×C3×#1142 | 2 |
| #10620893 | 2 |
| C7×#832 | 2 |
| #10620523 | 2 |
| #10620506 | 2 |
| #10620489 | 2 |
| #89529 | 3 |
| #5164 | 7 |