Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
164 conjugacy classes of subgroups; only the 49 normal subgroups are shown.
This group has 164 conjugacy classes of subgroups — too many to draw. Only its 49 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×C7×Q32 | C2 | semidirect |
| 3. #10620668 | C2 | semidirect |
| 4. Dic168 | C2 | semidirect |
| 15. C7×Q32 | D3 | semidirect |
| 35. C3×Q32 | D7 | semidirect |
| 60. D21 | Q32 | direct (N × H) |
| 64. Q32 | D21 | direct (N × H) |
| 78. C3×C7 | C2×Q32 | semidirect |
| 100. C7 | D3×Q32 | semidirect |
| 108. C3 | D7×Q32 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q16×D21 | 2 |
| C3×C7×Q32 | 2 |
| #10620668 | 2 |
| Dic168 | 2 |
| C16×D21 | 2 |
| D7×Q32 | 3 |
| D3×Q32 | 7 |