Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
532 conjugacy classes of subgroups; only the 211 normal subgroups are shown.
This group has 532 conjugacy classes of subgroups — too many to draw. Only its 211 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 |
|---|---|---|
| 2. C3×C4×C7×Q8 | C2 | semidirect |
| 3. Q8×Dic21 | C2 | semidirect |
| 5. #10621370 | C2 | semidirect |
| 7. C4×Dic42 | C2 | semidirect |
| 10. Q8×D21 | C4 | semidirect |
| 23. C4×C7×Q8 | D3 | semidirect |
| 54. C3×C4×Q8 | D7 | semidirect |
| 102. C4×Q8 | D21 | semidirect |
| 125. C3×C7 | #519 | semidirect |
| 163. C7 | #5572 | semidirect |
| 178. C3 | #90263 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q8×D21 | 2 |
| C3×C4×C7×Q8 | 2 |
| Q8×Dic21 | 2 |
| #10621375 | 2 |
| #10621370 | 2 |
| #10621355 | 2 |
| C4×Dic42 | 2 |
| #90263 | 3 |
| #5572 | 7 |