Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
240 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 240 conjugacy classes of subgroups — too many to draw. Only its 82 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 |
|---|---|---|
| 2. C2×C7×#214 | C2 | semidirect |
| 3. C7×#924 | C2 | semidirect |
| 4. C2×C7×#208 | C2 | semidirect |
| 5. C7×#832 | C2 | semidirect |
| 6. C7×#810 | C2 | semidirect |
| 7. C7×#807 | C2 | semidirect |
| 29. #5042 | C7 | direct (N × H) |
| 45. C7×C3⋊C8 | D4 | semidirect |
| 60. C2×#214 | C2×C7 | semidirect |
| 61. #924 | C2×C7 | semidirect |
| 62. C2×#208 | C2×C7 | semidirect |
| 63. #832 | C2×C7 | semidirect |
| 64. #810 | C2×C7 | semidirect |
| 65. #807 | C2×C7 | semidirect |
| 149. C3⋊C8 | C7×D4 | semidirect |
| 150. C3×C7 | #468 | semidirect |
| 198. C7 | #5042 | direct (N × H) |
| 217. C3 | C7×#468 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C7×#121 | 2 |
| C2×C7×#214 | 2 |
| C7×#924 | 2 |
| C2×C7×#208 | 2 |
| C7×#832 | 2 |
| C7×#810 | 2 |
| C7×#807 | 2 |
| C7×#468 | 3 |
| #5042 | 7 |