Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
364 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 364 conjugacy classes of subgroups — too many to draw. Only its 97 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×#3162 | C2 | semidirect |
| 4. #11725533 | C2 | semidirect |
| 5. #11725469 | C2 | semidirect |
| 28. C2×Dic28 | Q8 | semidirect |
| 31. C2×D56 | Q8 | semidirect |
| 44. #3162 | D7 | semidirect |
| 218. C7 | #13373 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#3162 | 2 |
| #11728410 | 2 |
| #11727599 | 2 |
| #11725533 | 2 |
| #11725469 | 2 |
| #13373 | 7 |