Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
164 conjugacy classes of subgroups; only the 56 normal subgroups are shown.
This group has 164 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 |
|---|---|---|
| 2. C2×C3×Dic28 | C2 | semidirect |
| 3. C7×#812 | C2 | semidirect |
| 4. #10620482 | C2 | semidirect |
| 5. #10620478 | C2 | semidirect |
| 16. C2×Dic28 | D3 | semidirect |
| 45. #812 | D7 | semidirect |
| 96. C3×C7 | #510 | semidirect |
| 125. C7 | #5179 | semidirect |
| 135. C3 | #89681 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10621387 | 2 |
| C2×C3×Dic28 | 2 |
| C7×#812 | 2 |
| #10620482 | 2 |
| #10620478 | 2 |
| #89681 | 3 |
| #5179 | 7 |