Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
240 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 240 conjugacy classes of subgroups — too many to draw. Only its 66 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. C2×#66627 | C2 | semidirect |
| 3. C3×#6487 | C2 | semidirect |
| 4. C2×#66564 | C2 | semidirect |
| 5. #10620524 | C2 | semidirect |
| 6. #10620505 | C2 | semidirect |
| 7. #10620501 | C2 | semidirect |
| 24. #6487 | D3 | semidirect |
| 45. C3⋊(C7⋊C8) | D4 | semidirect |
| 150. C3×C7 | #468 | semidirect |
| 198. C7 | #5049 | semidirect |
| 217. C3 | #89814 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#66627 | 2 |
| C7×#930 | 2 |
| C3×#6487 | 2 |
| C2×#66564 | 2 |
| #10620524 | 2 |
| #10620505 | 2 |
| #10620501 | 2 |
| #89814 | 3 |
| #5049 | 7 |