Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
216 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 77 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. #10621352 | C2 | semidirect |
| 3. C3×C7×C4⋊C8 | C2 | semidirect |
| 5. #10620657 | C2 | semidirect |
| 18. C7×C4⋊C8 | D3 | semidirect |
| 29. D84 | Q8 | semidirect |
| 44. C3×C4⋊C8 | D7 | semidirect |
| 85. C4⋊C8 | D21 | semidirect |
| 108. C3×C7 | #474 | semidirect |
| 143. C7 | #4846 | semidirect |
| 158. C3 | #89618 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×D84 | 2 |
| #10621352 | 2 |
| C3×C7×C4⋊C8 | 2 |
| #10620660 | 2 |
| #10620657 | 2 |
| #89618 | 3 |
| #4846 | 7 |