Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
424 conjugacy classes of subgroups; only the 147 normal subgroups are shown.
This group has 424 conjugacy classes of subgroups — too many to draw. Only its 147 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 |
|---|---|---|
| 3. #10621409 | C2 | semidirect |
| 4. #10621407 | C2 | semidirect |
| 5. #10621370 | C2 | semidirect |
| 6. #10621362 | C2 | semidirect |
| 7. #10621352 | C2 | semidirect |
| 8. C4×Dic42 | C2 | semidirect |
| 146. C3×C7 | #556 | semidirect |
| 190. C7 | #5542 | semidirect |
| 206. C3 | #90233 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C4×C7×D4 | 2 |
| #10621419 | 2 |
| #10621409 | 2 |
| #10621407 | 2 |
| #10621370 | 2 |
| #10621362 | 2 |
| #10621352 | 2 |
| C4×Dic42 | 2 |
| #90233 | 3 |
| #5542 | 7 |