Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
596 conjugacy classes of subgroups; only the 251 normal subgroups are shown.
This group has 596 conjugacy classes of subgroups — too many to draw. Only its 251 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 |
|---|---|---|
| 6. #10621370 | C2 | direct (N × H) |
| 13. C2×Dic42 | C4 | semidirect |
| 33. C2×Dic21 | Q8 | semidirect |
| 37. Dic42 | C2×C4 | semidirect |
| 63. Dic21 | C2×Q8 | semidirect |
| 88. C2×C3×C7 | C4×Q8 | semidirect |
| 119. C3×C7 | C2×C4×Q8 | semidirect |
| 131. C2×C7 | #887 | semidirect |
| 156. C7 | C2×#887 | semidirect |
| 157. C2×C3 | #6450 | semidirect |
| 170. C3 | C2×#6450 | semidirect |
| 171. C2 | #10621370 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×Dic42 | 2 |
| C2×C3×C7×C4⋊C4 | 2 |
| C2×#66629 | 2 |
| C2×C4×Dic21 | 2 |
| #10621370 | 2 |
| C2×#6450 | 3 |
| C2×#887 | 7 |