Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
260 conjugacy classes of subgroups; only the 62 normal subgroups are shown.
This group has 260 conjugacy classes of subgroups — too many to draw. Only its 62 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×#895 | C2 | semidirect |
| 2. #10621018 | C2 | semidirect |
| 3. C2×#66560 | C2 | semidirect |
| 4. C2×#66558 | C2 | semidirect |
| 5. #10620647 | C2 | semidirect |
| 6. C3×#6383 | C2 | semidirect |
| 7. #10620502 | C2 | semidirect |
| 27. #6383 | D3 | semidirect |
| 45. C3⋊(C7⋊C8) | D4 | semidirect |
| 63. #895 | D7 | semidirect |
| 158. C3×C7 | #469 | semidirect |
| 210. C7 | #4782 | semidirect |
| 232. C3 | #89811 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#895 | 2 |
| #10621018 | 2 |
| C2×#66560 | 2 |
| C2×#66558 | 2 |
| #10620647 | 2 |
| C3×#6383 | 2 |
| #10620502 | 2 |
| #89811 | 3 |
| #4782 | 7 |