Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
256 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 256 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 |
|---|---|---|
| 1. C2×#66623 | C2 | semidirect |
| 3. C4×Dic42 | C2 | semidirect |
| 4. C3×C7×C4⋊C8 | C2 | semidirect |
| 5. #10620660 | C2 | semidirect |
| 20. C7×C4⋊C8 | D3 | semidirect |
| 34. Dic42 | D4 | semidirect |
| 49. C3×C4⋊C8 | D7 | semidirect |
| 56. C3×C4×C7 | SD16 | semidirect |
| 92. C4⋊C8 | D21 | semidirect |
| 99. C4×C7 | #204 | semidirect |
| 117. C3×C7 | #460 | semidirect |
| 137. C3×C4 | #1132 | semidirect |
| 155. C7 | #4848 | semidirect |
| 167. C4 | #66623 | semidirect |
| 170. C3 | #89620 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#66623 | 2 |
| #10621357 | 2 |
| C4×Dic42 | 2 |
| C3×C7×C4⋊C8 | 2 |
| #10620660 | 2 |
| #89620 | 3 |
| #4848 | 7 |