Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
216 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 72 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. #10621031 | C2 | semidirect |
| 5. #10620521 | C2 | semidirect |
| 6. #10620520 | C2 | semidirect |
| 7. Dic3⋊(C7⋊C8) | C2 | semidirect |
| 30. C3×C7×D4 | Q8 | semidirect |
| 73. C7×D4 | Dic6 | semidirect |
| 119. C3×D4 | Dic14 | semidirect |
| 130. C3×C7 | #476 | semidirect |
| 160. D4 | #4248 | semidirect |
| 170. C7 | #4761 | semidirect |
| 186. C3 | #89780 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×D4×Dic3 | 2 |
| #10621031 | 2 |
| #10620671 | 2 |
| C3×#6406 | 2 |
| #10620521 | 2 |
| #10620520 | 2 |
| Dic3⋊(C7⋊C8) | 2 |
| #89780 | 3 |
| #4761 | 7 |