Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
164 conjugacy classes of subgroups; only the 44 normal subgroups are shown.
This group has 164 conjugacy classes of subgroups — too many to draw. Only its 44 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. Q16×D21 | C2 | semidirect |
| 3. C7×#828 | C2 | semidirect |
| 4. C3×#6403 | C2 | semidirect |
| 5. #10620482 | C2 | semidirect |
| 6. #10620479 | C2 | semidirect |
| 7. #10620471 | C2 | semidirect |
| 23. #6403 | D3 | semidirect |
| 54. #828 | D7 | semidirect |
| 115. C3×C7 | #510 | semidirect |
| 148. C7 | #4918 | semidirect |
| 159. C3 | #89687 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q16×D21 | 2 |
| #10620841 | 2 |
| C7×#828 | 2 |
| C3×#6403 | 2 |
| #10620482 | 2 |
| #10620479 | 2 |
| #10620471 | 2 |
| #89687 | 3 |
| #4918 | 7 |