Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
168 conjugacy classes of subgroups; only the 47 normal subgroups are shown.
This group has 168 conjugacy classes of subgroups — too many to draw. Only its 47 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. #10621395 | C2 | semidirect |
| 2. C3×C7×D16 | C2 | semidirect |
| 3. #10620666 | C2 | semidirect |
| 4. Dic168 | C2 | semidirect |
| 5. C16×D21 | C2 | semidirect |
| 15. C7×D16 | D3 | semidirect |
| 35. C3×D16 | D7 | semidirect |
| 65. D16 | D21 | semidirect |
| 79. C3×C7 | #508 | semidirect |
| 102. C7 | #4912 | semidirect |
| 111. C3 | #89684 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10621395 | 2 |
| C3×C7×D16 | 2 |
| #10620666 | 2 |
| Dic168 | 2 |
| C16×D21 | 2 |
| #89684 | 3 |
| #4912 | 7 |