Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
224 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 224 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 |
|---|---|---|
| 2. C2×C7×#216 | C2 | semidirect |
| 4. C7×#887 | C2 | semidirect |
| 5. C3×C7×#103 | C2 | semidirect |
| 6. C7×Dic3⋊C8 | C2 | semidirect |
| 27. C7×#103 | D3 | semidirect |
| 29. #4798 | C7 | direct (N × H) |
| 59. C2×#216 | C2×C7 | semidirect |
| 61. #887 | C2×C7 | semidirect |
| 62. C3×#103 | C2×C7 | semidirect |
| 63. Dic3⋊C8 | C2×C7 | semidirect |
| 114. #103 | D3×C7 | semidirect |
| 142. C3×C7 | #464 | semidirect |
| 186. C7 | #4798 | direct (N × H) |
| 202. C3 | C7×#464 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#947 | 2 |
| C2×C7×#216 | 2 |
| C2×C7×#204 | 2 |
| C7×#887 | 2 |
| C3×C7×#103 | 2 |
| C7×Dic3⋊C8 | 2 |
| C7×#809 | 2 |
| C7×#464 | 3 |
| #4798 | 7 |