Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
196 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 196 conjugacy classes of subgroups — too many to draw. Only its 75 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 |
|---|---|---|
| 25. C3×C7×C8 | Q8 | semidirect |
| 26. C3⋊(C7⋊C8) | Q8 | semidirect |
| 51. C7×C8 | Dic6 | semidirect |
| 78. C3×C8 | Dic14 | semidirect |
| 80. C3×C7 | #498 | semidirect |
| 102. C8 | Dic42 | semidirect |
| 103. C7 | #4855 | semidirect |
| 112. C3 | #89627 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10621371 | 2 |
| C3×C7×#106 | 2 |
| #10620656 | 2 |
| C8×Dic21 | 2 |
| #10620647 | 2 |
| #89627 | 3 |
| #4855 | 7 |