Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
282 conjugacy classes of subgroups; only the 47 normal subgroups are shown.
This group has 282 conjugacy classes of subgroups — too many to draw. Only its 47 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. #10621502 | C2 | direct (N × H) |
| 3. C2×C7⋊#226 | C2 | semidirect |
| 8. C7⋊#226 | C22 | semidirect |
| 99. C2×C7 | #984 | semidirect |
| 119. C7 | C2×#984 | semidirect |
| 131. C2 | #10621502 | 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 |
| #10621502 | 2 |
| C2×C7⋊#226 | 2 |
| C2×#6514 | 3 |
| C2×Dic42 | 4 |
| C2×#984 | 7 |