Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
260 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 260 conjugacy classes of subgroups — too many to draw. Only its 66 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. #10621430 | C2 | semidirect |
| 2. C2×C7×#215 | C2 | semidirect |
| 3. C2×C3×#1144 | C2 | semidirect |
| 4. #10620932 | C2 | semidirect |
| 5. C2×#66566 | C2 | semidirect |
| 7. #10620486 | C2 | semidirect |
| 24. C2×#1144 | D3 | semidirect |
| 63. C2×#215 | D7 | semidirect |
| 143. C3×C7 | #495 | semidirect |
| 187. C7 | #5191 | semidirect |
| 202. C3 | #89940 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10621430 | 2 |
| C2×C7×#215 | 2 |
| C2×C3×#1144 | 2 |
| #10620932 | 2 |
| C2×#66566 | 2 |
| C2×#66562 | 2 |
| #10620486 | 2 |
| #89940 | 3 |
| #5191 | 7 |