Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
216 conjugacy classes of subgroups; only the 54 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 54 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 |
|---|---|---|
| 1. #10621391 | C2 | semidirect |
| 2. #10620866 | C2 | semidirect |
| 3. C2×#66562 | C2 | semidirect |
| 4. #10620852 | C2 | semidirect |
| 5. C7×#823 | C2 | semidirect |
| 6. C3×#6396 | C2 | semidirect |
| 7. #10620495 | C2 | semidirect |
| 30. #6396 | D3 | semidirect |
| 69. #823 | D7 | semidirect |
| 148. C3×C7 | #472 | semidirect |
| 194. C7 | #4897 | semidirect |
| 209. C3 | #89521 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10621391 | 2 |
| #10620866 | 2 |
| C2×#66562 | 2 |
| #10620852 | 2 |
| C7×#823 | 2 |
| C3×#6396 | 2 |
| #10620495 | 2 |
| #89521 | 3 |
| #4897 | 7 |