Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
292 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 292 conjugacy classes of subgroups — too many to draw. Only its 81 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×#1833 | C2 | semidirect |
| 5. #11725539 | C2 | semidirect |
| 6. #11725533 | C2 | semidirect |
| 7. #11725478 | C2 | semidirect |
| 54. #1833 | D7 | semidirect |
| 237. C7 | #13490 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#1833 | 2 |
| C2×#89290 | 2 |
| #11728406 | 2 |
| #11727657 | 2 |
| #11725539 | 2 |
| #11725533 | 2 |
| #11725478 | 2 |
| #13490 | 7 |