Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
180 conjugacy classes of subgroups; only the 92 normal subgroups are shown.
This group has 180 conjugacy classes of subgroups — too many to draw. Only its 92 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 |
|---|---|---|
| 96. C3×C7 | #341 | semidirect |
| 129. C7 | #4558 | semidirect |
| 142. C3 | #89353 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C3⋊(C7⋊C8) | 2 |
| C2×C7×#208 | 2 |
| C2×C3×#1136 | 2 |
| #89353 | 3 |
| #4558 | 7 |