Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
476 conjugacy classes of subgroups; only the 108 normal subgroups are shown.
This group has 476 conjugacy classes of subgroups — too many to draw. Only its 108 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. C2×C7×Dic3⋊C4 | C2 | semidirect |
| 3. C2×(C2×D7)⋊Dic3 | C2 | semidirect |
| 4. C2×(C2×D7)⋊Dic3 | C2 | semidirect |
| 5. #10620670 | C2 | semidirect |
| 40. C2×C7×Dic3 | D4 | semidirect |
| 55. C2×Dic3⋊C4 | D7 | semidirect |
| 148. C2×Dic3 | D28 | semidirect |
| 149. C3×C7 | #394 | semidirect |
| 201. C7 | #5222 | semidirect |
| 224. C3 | #89763 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C3×D28 | 2 |
| C2×C7×Dic3⋊C4 | 2 |
| C2×(C2×D7)⋊Dic3 | 2 |
| #10620670 | 2 |
| #89763 | 3 |
| #5222 | 7 |