Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
216 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 216 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 |
|---|---|---|
| 72. C3×Dic7 | Q16 | semidirect |
| 121. Dic7 | #216 | semidirect |
| 137. C3×C7 | #462 | semidirect |
| 178. C7 | #5031 | semidirect |
| 191. C3 | #89954 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#66635 | 2 |
| C2×C7×#216 | 2 |
| C3×Q8×Dic7 | 2 |
| #10620938 | 2 |
| Dic7⋊(C3⋊C8) | 2 |
| #10620509 | 2 |
| #10620507 | 2 |
| #89954 | 3 |
| #5031 | 7 |