Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
380 conjugacy classes of subgroups; only the 112 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 112 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×#66627 | C2 | semidirect |
| 3. C7×#926 | C2 | semidirect |
| 4. #10620499 | C2 | semidirect |
| 10. C2×C3×D28 | C4 | semidirect |
| 13. C2×C3⋊(C7⋊C8) | C22 | semidirect |
| 15. C7×C4⋊Dic3 | C22 | semidirect |
| 39. C2×D28 | Dic3 | semidirect |
| 47. #926 | D7 | semidirect |
| 81. C4⋊Dic3 | C2×D7 | semidirect |
| 116. C3×C7 | #418 | semidirect |
| 155. C7 | #5215 | semidirect |
| 170. C3 | #89773 | 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×#66627 | 2 |
| C7×#926 | 2 |
| #10620499 | 2 |
| #89773 | 3 |
| #5215 | 7 |