Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
228 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 228 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 |
|---|---|---|
| 2. C2×C3×C4⋊Dic7 | C2 | semidirect |
| 3. #10620669 | C2 | semidirect |
| 4. #10620521 | C2 | semidirect |
| 5. #10620501 | C2 | semidirect |
| 17. C2×C4⋊Dic7 | D3 | semidirect |
| 111. C3×C7 | #481 | semidirect |
| 148. C7 | #4968 | semidirect |
| 165. C3 | #89806 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#930 | 2 |
| C2×C3×C4⋊Dic7 | 2 |
| #10620669 | 2 |
| #10620521 | 2 |
| #10620501 | 2 |
| #89806 | 3 |
| #4968 | 7 |