Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
260 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 260 conjugacy classes of subgroups — too many to draw. Only its 86 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×#124 | C2 | semidirect |
| 2. C2×C7×#216 | C2 | semidirect |
| 3. C2×C7×#215 | C2 | semidirect |
| 4. C2×C7×#214 | C2 | semidirect |
| 6. C7×#875 | C2 | semidirect |
| 7. C4×C7×C3⋊C8 | C2 | semidirect |
| 27. C7×#124 | D3 | semidirect |
| 29. #5059 | C7 | direct (N × H) |
| 59. C3×#124 | C2×C7 | semidirect |
| 60. C2×#216 | C2×C7 | semidirect |
| 61. C2×#215 | C2×C7 | semidirect |
| 62. C2×#214 | C2×C7 | semidirect |
| 64. #875 | C2×C7 | semidirect |
| 65. C4×C3⋊C8 | C2×C7 | semidirect |
| 115. #124 | D3×C7 | semidirect |
| 143. C3×C7 | #495 | semidirect |
| 187. C7 | #5059 | direct (N × H) |
| 202. C3 | C7×#495 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C7×#124 | 2 |
| C2×C7×#216 | 2 |
| C2×C7×#215 | 2 |
| C2×C7×#214 | 2 |
| C2×C7×#213 | 2 |
| C7×#875 | 2 |
| C4×C7×C3⋊C8 | 2 |
| C7×#495 | 3 |
| #5059 | 7 |