Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
292 conjugacy classes of subgroups; only the 142 normal subgroups are shown.
This group has 292 conjugacy classes of subgroups — too many to draw. Only its 142 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 |
|---|---|---|
| 3. C7×#836 | C2 | direct (N × H) |
| 17. C2×#836 | C7 | direct (N × H) |
| 40. #836 | C2×C7 | direct (N × H) |
| 71. C2×C3×C7 | #101 | semidirect |
| 94. C3×C7 | C2×#101 | semidirect |
| 106. C2×C7 | #836 | direct (N × H) |
| 126. C7 | C2×#836 | direct (N × H) |
| 129. C2×C3 | C7×#101 | semidirect |
| 138. C3 | C2×C7×#101 | semidirect |
| 141. C2 | C7×#836 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C3×C7×Q8 | 2 |
| C2×C7×#208 | 2 |
| C7×#836 | 2 |
| C2×C7×#101 | 3 |
| C2×#836 | 7 |