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 |
|---|---|---|
| 1. C7×#944 | C2 | semidirect |
| 5. C3×C7×#103 | C2 | semidirect |
| 6. C7×Dic3⋊C8 | C2 | semidirect |
| 7. C7×#810 | C2 | semidirect |
| 28. C7×#103 | D3 | semidirect |
| 29. #4818 | C7 | direct (N × H) |
| 59. #944 | C2×C7 | semidirect |
| 63. C3×#103 | C2×C7 | semidirect |
| 64. Dic3⋊C8 | C2×C7 | semidirect |
| 65. #810 | C2×C7 | semidirect |
| 76. C7×Dic3 | SD16 | semidirect |
| 117. #103 | D3×C7 | semidirect |
| 145. C3×C7 | #461 | semidirect |
| 173. Dic3 | C7×SD16 | semidirect |
| 190. C7 | #4818 | direct (N × H) |
| 206. C3 | C7×#461 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#944 | 2 |
| C2×C7×#215 | 2 |
| C2×C7×#204 | 2 |
| C7×#893 | 2 |
| C3×C7×#103 | 2 |
| C7×Dic3⋊C8 | 2 |
| C7×#810 | 2 |
| C7×#461 | 3 |
| #4818 | 7 |