Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
248 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 248 conjugacy classes of subgroups — too many to draw. Only its 69 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. C2×#66623 | C2 | semidirect |
| 3. #10621358 | C2 | semidirect |
| 4. C4×D84 | C2 | semidirect |
| 5. C3×C7×C4⋊C8 | C2 | semidirect |
| 6. #10620660 | C2 | semidirect |
| 7. #10620655 | C2 | semidirect |
| 26. C7×C4⋊C8 | D3 | semidirect |
| 63. C3×C4⋊C8 | D7 | semidirect |
| 118. C4⋊C8 | D21 | semidirect |
| 150. C3×C7 | #463 | semidirect |
| 198. C7 | #4844 | semidirect |
| 217. C3 | #89616 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D168 | 2 |
| C2×#66623 | 2 |
| #10621358 | 2 |
| C4×D84 | 2 |
| C3×C7×C4⋊C8 | 2 |
| #10620660 | 2 |
| #10620655 | 2 |
| #89616 | 3 |
| #4844 | 7 |