Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
292 conjugacy classes of subgroups; only the 92 normal subgroups are shown.
This group has 292 conjugacy classes of subgroups — too many to draw. Only its 92 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. #10620675 | C2 | semidirect |
| 4. C7×#836 | C2 | semidirect |
| 5. #10620496 | C2 | semidirect |
| 53. #836 | D7 | direct (N × H) |
| 91. C3×D7 | #101 | semidirect |
| 119. C3×C7 | C2×#101 | semidirect |
| 134. D7 | #836 | direct (N × H) |
| 157. C7 | C2×#836 | semidirect |
| 170. C3 | D7×#101 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×Q8×D7 | 2 |
| D7×#208 | 2 |
| #10620675 | 2 |
| C7×#836 | 2 |
| #10620496 | 2 |
| D7×#101 | 3 |
| C2×#836 | 7 |