Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
596 conjugacy classes of subgroups; only the 280 normal subgroups are shown.
This group has 596 conjugacy classes of subgroups — too many to draw. Only its 280 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. #10620906 | C2 | direct (N × H) |
| 12. C2×C7×Dic6 | C4 | semidirect |
| 30. C2×Dic21 | Q8 | semidirect |
| 35. C7×Dic6 | C2×C4 | semidirect |
| 61. Dic21 | C2×Q8 | semidirect |
| 82. C2×Dic6 | Dic7 | semidirect |
| 88. C2×C3×C7 | C4×Q8 | semidirect |
| 118. Dic6 | C2×Dic7 | semidirect |
| 119. C3×C7 | C2×C4×Q8 | semidirect |
| 131. C2×C7 | #887 | semidirect |
| 156. C7 | C2×#887 | semidirect |
| 157. C2×C3 | Q8×Dic7 | semidirect |
| 170. C3 | C2×Q8×Dic7 | semidirect |
| 171. C2 | #10620906 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C7×Dic6 | 2 |
| C2×C4×Dic21 | 2 |
| C2×C3×C4⋊Dic7 | 2 |
| C2×Dic3⋊Dic7 | 2 |
| C2×Dic3×Dic7 | 2 |
| #10620906 | 2 |
| C2×Q8×Dic7 | 3 |
| C2×#887 | 7 |