Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
404 conjugacy classes of subgroups; only the 122 normal subgroups are shown.
This group has 404 conjugacy classes of subgroups — too many to draw. Only its 122 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 |
|---|---|---|
| 1. C22×C3×Dic14 | C2 | semidirect |
| 4. C3×C7×#95 | C2 | semidirect |
| 5. C3×C7⋊#95 | C2 | semidirect |
| 6. #89445 | C3 | direct (N × H) |
| 16. C22×Dic14 | C2×C3 | semidirect |
| 19. C7×#95 | C2×C3 | semidirect |
| 20. C7⋊#95 | C2×C3 | semidirect |
| 27. C22×C3×D7 | Q8 | semidirect |
| 52. C3×#95 | D7 | semidirect |
| 73. C22×D7 | C3×Q8 | semidirect |
| 104. #95 | C3×D7 | semidirect |
| 136. C3×C7 | #393 | semidirect |
| 183. C7 | C3×#393 | semidirect |
| 204. C3 | #89445 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C3×Dic14 | 2 |
| C2×C3×(C2×D7)⋊C4 | 2 |
| C3×C7×#95 | 2 |
| C3×C7⋊#95 | 2 |
| #89445 | 3 |
| C3×#393 | 7 |