Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
164 conjugacy classes of subgroups; only the 47 normal subgroups are shown.
This group has 164 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 |
|---|---|---|
| 2. Q16×D21 | C2 | semidirect |
| 3. C3×C7×Q32 | C2 | semidirect |
| 4. #10620668 | C2 | semidirect |
| 5. #10620667 | C2 | semidirect |
| 6. #10620639 | C2 | semidirect |
| 7. #10620637 | C2 | semidirect |
| 22. C7×Q32 | D3 | semidirect |
| 52. C3×Q32 | D7 | semidirect |
| 93. Q32 | D21 | semidirect |
| 115. C3×C7 | #510 | semidirect |
| 148. C7 | #4918 | semidirect |
| 159. C3 | #89690 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10621402 | 2 |
| Q16×D21 | 2 |
| C3×C7×Q32 | 2 |
| #10620668 | 2 |
| #10620667 | 2 |
| #10620639 | 2 |
| #10620637 | 2 |
| #89690 | 3 |
| #4918 | 7 |