Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
476 conjugacy classes of subgroups; only the 106 normal subgroups are shown.
This group has 476 conjugacy classes of subgroups — too many to draw. Only its 106 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×#66629 | C2 | semidirect |
| 3. C2×(C2×D7)⋊Dic3 | C2 | semidirect |
| 4. C2×(C2×D7)⋊Dic3 | C2 | semidirect |
| 5. C7×C3⋊#95 | C2 | semidirect |
| 37. C2×Dic21 | D4 | semidirect |
| 56. C3⋊#95 | D7 | semidirect |
| 149. C3×C7 | #394 | semidirect |
| 201. C7 | #5222 | semidirect |
| 224. C3 | #89444 | 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×#66629 | 2 |
| C2×(C2×D7)⋊Dic3 | 2 |
| C7×C3⋊#95 | 2 |
| #89444 | 3 |
| #5222 | 7 |