Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
244 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 244 conjugacy classes of subgroups — too many to draw. Only its 79 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. #10621370 | C2 | semidirect |
| 5. #10620655 | C2 | semidirect |
| 6. C8×Dic21 | C2 | semidirect |
| 7. #10620647 | C2 | semidirect |
| 15. #66633 | C4 | semidirect |
| 40. Dic42 | C2×C4 | semidirect |
| 42. C3⋊(C7⋊C8) | C2×C4 | semidirect |
| 72. Dic21 | SD16 | semidirect |
| 136. C3×C7 | C4×SD16 | semidirect |
| 178. C7 | #4758 | semidirect |
| 194. C3 | #89530 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D4×Dic21 | 2 |
| C2×#66633 | 2 |
| #10621370 | 2 |
| C3×C7×#102 | 2 |
| #10620655 | 2 |
| C8×Dic21 | 2 |
| #10620647 | 2 |
| #89530 | 3 |
| #4758 | 7 |