Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
260 conjugacy classes of subgroups; only the 94 normal subgroups are shown.
This group has 260 conjugacy classes of subgroups — too many to draw. Only its 94 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. C2×C3×Dic28 | C2 | semidirect |
| 3. C2×C3×#1132 | C2 | semidirect |
| 4. C3×#6438 | C2 | semidirect |
| 5. C3×C4×C7×C8 | C2 | semidirect |
| 6. #89468 | C3 | direct (N × H) |
| 16. C2×Dic28 | C2×C3 | semidirect |
| 18. C2×#1132 | C2×C3 | semidirect |
| 19. #6438 | C2×C3 | semidirect |
| 20. C4×C7×C8 | C2×C3 | semidirect |
| 45. C3×C4×C8 | D7 | semidirect |
| 80. C4×C8 | C3×D7 | semidirect |
| 98. C3×C7 | #495 | semidirect |
| 128. C7 | C3×#495 | semidirect |
| 139. C3 | #89468 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×Dic28 | 2 |
| C2×C3×D56 | 2 |
| C2×C3×#1132 | 2 |
| C3×#6438 | 2 |
| C3×C4×C7×C8 | 2 |
| #89468 | 3 |
| C3×#495 | 7 |