Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
268 conjugacy classes of subgroups; only the 68 normal subgroups are shown.
This group has 268 conjugacy classes of subgroups — too many to draw. Only its 68 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. C7×#938 | C2 | semidirect |
| 2. C2×C3×#1141 | C2 | semidirect |
| 3. #10621018 | C2 | semidirect |
| 4. C2×D3×C7⋊C8 | C2 | semidirect |
| 5. #10620671 | C2 | semidirect |
| 6. #10620523 | C2 | semidirect |
| 7. #10620499 | C2 | semidirect |
| 23. C2×#1141 | D3 | semidirect |
| 46. C3×C7⋊C8 | D4 | semidirect |
| 62. #938 | D7 | semidirect |
| 73. C2×D3×C7 | D8 | semidirect |
| 99. C7⋊C8 | #67 | semidirect |
| 158. C3×C7 | #466 | semidirect |
| 187. C2×D3 | #1141 | semidirect |
| 210. C7 | #5157 | semidirect |
| 232. C3 | #89810 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#938 | 2 |
| C2×C3×#1141 | 2 |
| #10621018 | 2 |
| C2×D3×C7⋊C8 | 2 |
| #10620671 | 2 |
| #10620523 | 2 |
| #10620499 | 2 |
| #89810 | 3 |
| #5157 | 7 |