Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
248 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 248 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×#66634 | C2 | semidirect |
| 2. C7×#946 | C2 | semidirect |
| 4. C2×D3×C7⋊C8 | C2 | semidirect |
| 5. C3×#6409 | C2 | semidirect |
| 6. #10620521 | C2 | semidirect |
| 7. #10620504 | C2 | semidirect |
| 26. #6409 | D3 | semidirect |
| 44. C3⋊(C7⋊C8) | D4 | semidirect |
| 59. #946 | D7 | semidirect |
| 72. C2×D3×C7 | SD16 | semidirect |
| 150. C3×C7 | #465 | semidirect |
| 175. C2×D3 | #1143 | semidirect |
| 198. C7 | #4807 | semidirect |
| 217. C3 | #89820 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#66634 | 2 |
| C7×#946 | 2 |
| #10621022 | 2 |
| C2×D3×C7⋊C8 | 2 |
| C3×#6409 | 2 |
| #10620521 | 2 |
| #10620504 | 2 |
| #89820 | 3 |
| #4807 | 7 |