Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
168 conjugacy classes of subgroups; only the 56 normal subgroups are shown.
This group has 168 conjugacy classes of subgroups — too many to draw. Only its 56 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. #10621387 | C2 | semidirect |
| 2. C3×#6467 | C2 | semidirect |
| 3. C2×C7×C3⋊C16 | C2 | semidirect |
| 4. #10620482 | C2 | semidirect |
| 5. #10620478 | C2 | semidirect |
| 6. #10620477 | C2 | semidirect |
| 7. #10620473 | C2 | semidirect |
| 21. #6467 | D3 | semidirect |
| 56. C2×C3⋊C16 | D7 | semidirect |
| 116. C3×C7 | #508 | semidirect |
| 150. C7 | #5194 | semidirect |
| 162. C3 | #89676 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10621387 | 2 |
| C3×#6467 | 2 |
| C2×C7×C3⋊C16 | 2 |
| #10620482 | 2 |
| #10620478 | 2 |
| #10620477 | 2 |
| #10620473 | 2 |
| #89676 | 3 |
| #5194 | 7 |