Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
280 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 280 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. C3×C7×#127 | C2 | semidirect |
| 2. C2×#66632 | C2 | semidirect |
| 3. C4×D84 | C2 | semidirect |
| 4. #10620671 | C2 | semidirect |
| 5. C4⋊(C3⋊(C7⋊C8)) | C2 | semidirect |
| 17. C7×#127 | D3 | semidirect |
| 34. D84 | D4 | semidirect |
| 47. C3×#127 | D7 | semidirect |
| 60. C3×C4×C7 | D8 | semidirect |
| 95. #127 | D21 | semidirect |
| 107. C4×C7 | #213 | semidirect |
| 125. C3×C7 | #459 | semidirect |
| 149. C3×C4 | #1141 | semidirect |
| 167. C7 | #5072 | semidirect |
| 182. C4 | #66632 | semidirect |
| 185. C3 | #89844 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C7×#127 | 2 |
| C2×#66632 | 2 |
| C4×D84 | 2 |
| #10620671 | 2 |
| C4⋊(C3⋊(C7⋊C8)) | 2 |
| #89844 | 3 |
| #5072 | 7 |