Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
256 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 256 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. C2×C7×#204 | C2 | semidirect |
| 4. C7×#887 | C2 | semidirect |
| 5. C3×C7×#102 | C2 | semidirect |
| 6. C7×Dic3⋊C8 | C2 | semidirect |
| 7. C7×#809 | C2 | semidirect |
| 28. C7×#102 | D3 | semidirect |
| 29. #4762 | C7 | direct (N × H) |
| 44. C7×Dic6 | D4 | semidirect |
| 61. C2×#214 | C2×C7 | semidirect |
| 62. C2×#204 | C2×C7 | semidirect |
| 63. #887 | C2×C7 | semidirect |
| 64. C3×#102 | C2×C7 | semidirect |
| 65. Dic3⋊C8 | C2×C7 | semidirect |
| 66. #809 | C2×C7 | semidirect |
| 79. C7×Dic3 | SD16 | semidirect |
| 122. #102 | D3×C7 | semidirect |
| 150. Dic6 | C7×D4 | semidirect |
| 153. C3×C7 | #460 | semidirect |
| 184. Dic3 | C7×SD16 | semidirect |
| 202. C7 | #4762 | direct (N × H) |
| 221. C3 | C7×#460 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#940 | 2 |
| C2×C7×#214 | 2 |
| C2×C7×#204 | 2 |
| C7×#887 | 2 |
| C3×C7×#102 | 2 |
| C7×Dic3⋊C8 | 2 |
| C7×#809 | 2 |
| C7×#460 | 3 |
| #4762 | 7 |