Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
572 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 572 conjugacy classes of subgroups — too many to draw. Only its 85 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×#3112 | C2 | semidirect |
| 3. #11739929 | C2 | semidirect |
| 4. #11729572 | C2 | semidirect |
| 5. #11729377 | C2 | semidirect |
| 6. #11728558 | C2 | semidirect |
| 7. #11725555 | C2 | semidirect |
| 85. #3112 | D7 | semidirect |
| 401. C7 | #10006 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#3112 | 2 |
| #11740751 | 2 |
| #11739929 | 2 |
| #11729572 | 2 |
| #11729377 | 2 |
| #11728558 | 2 |
| #11725555 | 2 |
| #10006 | 7 |