Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
464 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 464 conjugacy classes of subgroups — too many to draw. Only its 87 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×#2134 | C2 | semidirect |
| 3. #11729613 | C2 | semidirect |
| 4. #11727903 | C2 | semidirect |
| 5. #11727900 | C2 | semidirect |
| 6. #11727888 | C2 | semidirect |
| 7. #11727887 | C2 | semidirect |
| 11. C22×#1141 | C4 | semidirect |
| 16. #89987 | C4 | semidirect |
| 23. #89773 | C4 | semidirect |
| 24. #89770 | C4 | semidirect |
| 85. #2134 | D7 | semidirect |
| 404. C7 | #13234 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11740823 | 2 |
| C7×#2134 | 2 |
| #11729613 | 2 |
| #11727903 | 2 |
| #11727900 | 2 |
| #11727888 | 2 |
| #11727887 | 2 |
| #13234 | 7 |