Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
484 conjugacy classes of subgroups; only the 171 normal subgroups are shown.
This group has 484 conjugacy classes of subgroups — too many to draw. Only its 171 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. #10621407 | C2 | semidirect |
| 4. #10621361 | C2 | semidirect |
| 9. C2×Dic42 | C22 | semidirect |
| 13. C4⋊Dic21 | C22 | semidirect |
| 14. #66629 | C22 | semidirect |
| 21. C23×C3×C7 | Q8 | semidirect |
| 52. C23×C7 | Dic6 | semidirect |
| 86. C23×C3 | Dic14 | semidirect |
| 94. C3×C7 | #543 | semidirect |
| 117. C23 | Dic42 | semidirect |
| 125. C7 | #5483 | semidirect |
| 138. C3 | #90174 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×C7×C22⋊C4 | 2 |
| C2×#66636 | 2 |
| #10621407 | 2 |
| #10621361 | 2 |
| #90174 | 3 |
| #5483 | 7 |