Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
196 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 196 conjugacy classes of subgroups — too many to draw. Only its 87 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 |
|---|---|---|
| 26. C3⋊(C7⋊C8) | Q8 | semidirect |
| 83. C3×C7 | #500 | semidirect |
| 109. C7 | #5078 | semidirect |
| 119. C3 | #89850 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C7×C4⋊Q8 | 2 |
| #10621352 | 2 |
| #10620646 | 2 |
| C4×C3⋊(C7⋊C8) | 2 |
| #89850 | 3 |
| #5078 | 7 |