Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
164 conjugacy classes of subgroups; only the 48 normal subgroups are shown.
This group has 164 conjugacy classes of subgroups — too many to draw. Only its 48 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. C3×D7×Q16 | C2 | semidirect |
| 3. #10620668 | C2 | semidirect |
| 4. C7×#828 | C2 | semidirect |
| 5. #10620482 | C2 | semidirect |
| 6. #10620476 | C2 | semidirect |
| 7. #10620469 | C2 | semidirect |
| 20. D7×Q16 | D3 | semidirect |
| 55. #828 | D7 | semidirect |
| 115. C3×C7 | #510 | semidirect |
| 148. C7 | #5179 | semidirect |
| 159. C3 | #89687 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×D7×Q16 | 2 |
| #10620832 | 2 |
| #10620668 | 2 |
| C7×#828 | 2 |
| #10620482 | 2 |
| #10620476 | 2 |
| #10620469 | 2 |
| #89687 | 3 |
| #5179 | 7 |