Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
192 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 192 conjugacy classes of subgroups — too many to draw. Only its 70 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. C7×#815 | C2 | semidirect |
| 4. C3×Dic7⋊C8 | C2 | semidirect |
| 5. Dic7⋊(C3⋊C8) | C2 | semidirect |
| 7. Dic3×C7⋊C8 | C2 | semidirect |
| 25. Dic7⋊C8 | D3 | semidirect |
| 56. #815 | D7 | semidirect |
| 130. C3×C7 | #433 | semidirect |
| 170. C7 | #4840 | semidirect |
| 186. C3 | #89481 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10620948 | 2 |
| #10620659 | 2 |
| C7×#815 | 2 |
| C3×Dic7⋊C8 | 2 |
| Dic7⋊(C3⋊C8) | 2 |
| #10620492 | 2 |
| Dic3×C7⋊C8 | 2 |
| #89481 | 3 |
| #4840 | 7 |