Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
220 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 220 conjugacy classes of subgroups — too many to draw. Only its 78 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. C3×C7×#125 | C2 | semidirect |
| 3. C3×#6383 | C2 | semidirect |
| 4. C3×#6377 | C2 | semidirect |
| 5. #89839 | C3 | direct (N × H) |
| 12. C7×#125 | C2×C3 | semidirect |
| 14. #6383 | C2×C3 | semidirect |
| 15. #6377 | C2×C3 | semidirect |
| 31. C3×#125 | D7 | semidirect |
| 58. #125 | C3×D7 | semidirect |
| 74. C3×C7 | #490 | semidirect |
| 97. C7 | C3×#490 | semidirect |
| 107. C3 | #89839 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C7×#125 | 2 |
| C3×#6437 | 2 |
| C3×#6383 | 2 |
| C3×#6377 | 2 |
| #89839 | 3 |
| C3×#490 | 7 |