Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
240 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 240 conjugacy classes of subgroups — too many to draw. Only its 72 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 |
|---|---|---|
| 4. #10620938 | C2 | semidirect |
| 5. Dic7⋊(C3⋊C8) | C2 | semidirect |
| 6. #10620509 | C2 | semidirect |
| 7. #10620507 | C2 | semidirect |
| 75. C3×Dic7 | SD16 | semidirect |
| 128. Dic7 | #214 | semidirect |
| 145. C3×C7 | #461 | semidirect |
| 190. C7 | #5019 | semidirect |
| 206. C3 | #89934 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#66633 | 2 |
| C2×C7×#214 | 2 |
| C3×D4×Dic7 | 2 |
| #10620938 | 2 |
| Dic7⋊(C3⋊C8) | 2 |
| #10620509 | 2 |
| #10620507 | 2 |
| #89934 | 3 |
| #5019 | 7 |