Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
220 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 220 conjugacy classes of subgroups — too many to draw. Only its 74 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. C7×#890 | C2 | semidirect |
| 3. C3×C7×#102 | C2 | semidirect |
| 4. C7×#832 | C2 | semidirect |
| 5. C7×#821 | C2 | semidirect |
| 6. C7×#815 | C2 | semidirect |
| 7. C7×#809 | C2 | semidirect |
| 25. C7×#102 | D3 | semidirect |
| 27. #4764 | C7 | direct (N × H) |
| 55. #890 | C2×C7 | semidirect |
| 56. C3×#102 | C2×C7 | semidirect |
| 57. #832 | C2×C7 | semidirect |
| 58. #821 | C2×C7 | semidirect |
| 59. #815 | C2×C7 | semidirect |
| 60. #809 | C2×C7 | semidirect |
| 111. #102 | D3×C7 | semidirect |
| 141. C3×C7 | #490 | semidirect |
| 186. C7 | #4764 | direct (N × H) |
| 205. C3 | C7×#490 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#940 | 2 |
| C7×#890 | 2 |
| C3×C7×#102 | 2 |
| C7×#832 | 2 |
| C7×#821 | 2 |
| C7×#815 | 2 |
| C7×#809 | 2 |
| C7×#490 | 3 |
| #4764 | 7 |