Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
128 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 128 conjugacy classes of subgroups — too many to draw. Only its 61 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 |
|---|---|---|
| 75. C3×C7 | #332 | semidirect |
| 100. C7 | #4486 | semidirect |
| 111. C3 | #89281 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10621352 | 2 |
| C3×C7×C4⋊C8 | 2 |
| C4⋊(C3⋊(C7⋊C8)) | 2 |
| #89281 | 3 |
| #4486 | 7 |