Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
564 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 564 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×#3135 | C2 | semidirect |
| 2. #11740800 | C2 | semidirect |
| 4. #11729592 | C2 | semidirect |
| 5. #11729568 | C2 | semidirect |
| 6. #11727577 | C2 | semidirect |
| 7. #11725467 | C2 | semidirect |
| 79. #3135 | D7 | semidirect |
| 362. C7 | #10219 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#3135 | 2 |
| #11740800 | 2 |
| #11740747 | 2 |
| #11729592 | 2 |
| #11729568 | 2 |
| #11727577 | 2 |
| #11725467 | 2 |
| #10219 | 7 |