Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
280 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 280 conjugacy classes of subgroups — too many to draw. Only its 74 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. C4×D84 | C2 | semidirect |
| 2. C3×#6437 | C2 | semidirect |
| 3. C2×#66561 | C2 | semidirect |
| 4. C7×C4⋊(C3⋊C8) | C2 | semidirect |
| 5. #10620500 | C2 | semidirect |
| 18. #6437 | D3 | semidirect |
| 30. D84 | D4 | semidirect |
| 51. C4⋊(C3⋊C8) | D7 | semidirect |
| 60. C3×C4×C7 | D8 | semidirect |
| 107. C4×C7 | #213 | semidirect |
| 125. C3×C7 | #459 | semidirect |
| 149. C3×C4 | D56 | semidirect |
| 167. C7 | #5072 | semidirect |
| 182. C4 | #66561 | semidirect |
| 185. C3 | #89615 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×D84 | 2 |
| C3×#6437 | 2 |
| C2×#66561 | 2 |
| C7×C4⋊(C3⋊C8) | 2 |
| #10620500 | 2 |
| #89615 | 3 |
| #5072 | 7 |