Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
228 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 228 conjugacy classes of subgroups — too many to draw. Only its 83 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. C3×C7×C4⋊C8 | C2 | semidirect |
| 5. #10620653 | C2 | semidirect |
| 6. #10620653 | C2 | semidirect |
| 7. C4⋊(C3⋊(C7⋊C8)) | C2 | semidirect |
| 25. C7×C4⋊C8 | D3 | semidirect |
| 59. C3×C4⋊C8 | D7 | semidirect |
| 111. C4⋊C8 | D21 | semidirect |
| 136. C3×C7 | #424 | semidirect |
| 178. C7 | #4839 | semidirect |
| 194. C3 | #89611 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#66622 | 2 |
| C2×C8×D21 | 2 |
| #10621355 | 2 |
| C3×C7×C4⋊C8 | 2 |
| #10620653 | 2 |
| C4⋊(C3⋊(C7⋊C8)) | 2 |
| #89611 | 3 |
| #4839 | 7 |