Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
372 conjugacy classes of subgroups; only the 155 normal subgroups are shown.
This group has 372 conjugacy classes of subgroups — too many to draw. Only its 155 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 |
|---|---|---|
| 12. C2×Dic42 | C4 | semidirect |
| 26. C2×C3×C4×C7 | Q8 | semidirect |
| 59. C2×C4×C7 | Dic6 | semidirect |
| 99. C2×C3×C4 | Dic14 | semidirect |
| 109. C3×C7 | #391 | semidirect |
| 142. C2×C4 | Dic42 | semidirect |
| 146. C7 | #4929 | semidirect |
| 161. C3 | #89701 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×Dic42 | 2 |
| C2×C3×C42×C7 | 2 |
| C2×C4⋊Dic21 | 2 |
| #10620670 | 2 |
| #89701 | 3 |
| #4929 | 7 |