Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
228 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 228 conjugacy classes of subgroups — too many to draw. Only its 131 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 |
|---|---|---|
| 4. C4⋊(C3⋊(C7⋊C8)) | C2 | semidirect |
| 85. C3×C7 | #424 | semidirect |
| 112. C7 | #4999 | semidirect |
| 123. C3 | #89771 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C7×#117 | 2 |
| C2×#66627 | 2 |
| C22×C3⋊(C7⋊C8) | 2 |
| C4⋊(C3⋊(C7⋊C8)) | 2 |
| #89771 | 3 |
| #4999 | 7 |