Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
288 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 288 conjugacy classes of subgroups — too many to draw. Only its 71 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×#66633 | C2 | semidirect |
| 3. C2×#66632 | C2 | semidirect |
| 4. #10621358 | C2 | semidirect |
| 5. #10620642 | C2 | semidirect |
| 16. C7×#127 | D3 | semidirect |
| 32. C3⋊(C7⋊C8) | D4 | semidirect |
| 42. C3×#127 | D7 | semidirect |
| 82. #127 | D21 | semidirect |
| 104. C3×C7 | #496 | semidirect |
| 137. C7 | #5074 | semidirect |
| 150. C3 | #89846 | 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×#66633 | 2 |
| C2×#66632 | 2 |
| #10621358 | 2 |
| #10620642 | 2 |
| #89846 | 3 |
| #5074 | 7 |