Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
240 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 240 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×#6509 | C2 | semidirect |
| 2. C2×C3×#1143 | C2 | semidirect |
| 3. C2×C3×#1131 | C2 | semidirect |
| 5. C3×C7×#103 | C2 | semidirect |
| 6. C3×#6395 | C2 | semidirect |
| 7. C3×#6381 | C2 | semidirect |
| 8. #89584 | C3 | direct (N × H) |
| 22. #6509 | C2×C3 | semidirect |
| 23. C2×#1143 | C2×C3 | semidirect |
| 24. C2×#1131 | C2×C3 | semidirect |
| 26. C7×#103 | C2×C3 | semidirect |
| 27. #6395 | C2×C3 | semidirect |
| 28. #6381 | C2×C3 | semidirect |
| 45. C3×C7⋊C8 | D4 | semidirect |
| 64. C3×#103 | D7 | semidirect |
| 95. C7⋊C8 | C3×D4 | semidirect |
| 119. #103 | C3×D7 | semidirect |
| 150. C3×C7 | #468 | semidirect |
| 198. C7 | C3×#468 | semidirect |
| 217. C3 | #89584 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#6509 | 2 |
| C2×C3×#1143 | 2 |
| C2×C3×#1131 | 2 |
| C3×#6458 | 2 |
| C3×C7×#103 | 2 |
| C3×#6395 | 2 |
| C3×#6381 | 2 |
| #89584 | 3 |
| C3×#468 | 7 |