Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
200 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 200 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×#888 | C2 | semidirect |
| 5. C7×#816 | C2 | semidirect |
| 6. C7×#815 | C2 | semidirect |
| 7. C7×#810 | C2 | semidirect |
| 27. #4765 | C7 | direct (N × H) |
| 54. #888 | C2×C7 | semidirect |
| 57. #816 | C2×C7 | semidirect |
| 58. #815 | C2×C7 | semidirect |
| 59. #810 | C2×C7 | semidirect |
| 133. C3×C7 | #489 | semidirect |
| 174. C7 | #4765 | direct (N × H) |
| 190. C3 | C7×#489 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#936 | 2 |
| C7×#888 | 2 |
| C3×C7×#102 | 2 |
| C7×#832 | 2 |
| C7×#816 | 2 |
| C7×#815 | 2 |
| C7×#810 | 2 |
| C7×#489 | 3 |
| #4765 | 7 |