Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
206 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 206 conjugacy classes of subgroups — too many to draw. Only its 91 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 |
|---|---|---|
| 3. C7×#1424 | C2 | semidirect |
| 4. #11725398 | C2 | semidirect |
| 5. #11725382 | C2 | semidirect |
| 13. D7×C32 | C4 | semidirect |
| 24. C7×C32 | C2×C4 | semidirect |
| 25. C7⋊C32 | C2×C4 | semidirect |
| 30. #1424 | D7 | direct (N × H) |
| 72. C32 | C4×D7 | semidirect |
| 95. D7 | #1424 | direct (N × H) |
| 107. C7 | C2×#1424 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D7×C32 | 2 |
| D7×#366 | 2 |
| C7×#1424 | 2 |
| #11725398 | 2 |
| #11725382 | 2 |
| C2×#1424 | 7 |