Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
220 conjugacy classes of subgroups; only the 76 normal subgroups are shown.
This group has 220 conjugacy classes of subgroups — too many to draw. Only its 76 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. C7×#803 | C2 | semidirect |
| 3. C3×#6377 | C2 | semidirect |
| 4. #10620518 | C2 | semidirect |
| 20. #6377 | D3 | semidirect |
| 47. #803 | D7 | semidirect |
| 111. C3×C7 | #432 | semidirect |
| 147. C7 | #4705 | semidirect |
| 162. C3 | #89477 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C42×D21 | 2 |
| C7×#803 | 2 |
| C3×#6377 | 2 |
| #10620518 | 2 |
| #10620492 | 2 |
| #89477 | 3 |
| #4705 | 7 |