Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
282 conjugacy classes of subgroups; only the 58 normal subgroups are shown.
This group has 282 conjugacy classes of subgroups — too many to draw. Only its 58 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 |
|---|---|---|
| 2. C7×#984 | C2 | direct (N × H) |
| 3. C2×C7×#226 | C2 | semidirect |
| 8. C7×#226 | C22 | semidirect |
| 16. C2×#984 | C7 | direct (N × H) |
| 37. #984 | C2×C7 | direct (N × H) |
| 38. C2×#226 | C2×C7 | semidirect |
| 61. #226 | C22×C7 | semidirect |
| 99. C2×C7 | #984 | direct (N × H) |
| 119. C7 | C2×#984 | direct (N × H) |
| 131. C2 | C7×#984 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C7×#41⋊C3 | 2 |
| C7×#984 | 2 |
| C2×C7×#226 | 2 |
| C2×C7×#137 | 3 |
| C2×C7×Dic6 | 4 |
| C2×#984 | 7 |