Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
690 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 690 conjugacy classes of subgroups — too many to draw. Only its 105 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×#3206 | C2 | semidirect |
| 3. #11740696 | C2 | semidirect |
| 4. #11729569 | C2 | semidirect |
| 5. #11729528 | C2 | semidirect |
| 6. #11728528 | C2 | semidirect |
| 7. #11725542 | C2 | semidirect |
| 72. #3206 | D7 | semidirect |
| 351. C7 | #10281 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#3206 | 2 |
| #11740747 | 2 |
| #11740696 | 2 |
| #11729569 | 2 |
| #11729528 | 2 |
| #11728528 | 2 |
| #11725542 | 2 |
| #10281 | 7 |