Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
302 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 302 conjugacy classes of subgroups — too many to draw. Only its 67 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×#3352 | C2 | semidirect |
| 2. #11729106 | C2 | semidirect |
| 3. #11728668 | C2 | semidirect |
| 5. #11725605 | C2 | semidirect |
| 6. #11725570 | C2 | semidirect |
| 7. #11725567 | C2 | semidirect |
| 62. #3352 | D7 | semidirect |
| 271. C7 | #12349 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#3352 | 2 |
| #11729106 | 2 |
| #11728668 | 2 |
| #11728622 | 2 |
| #11725605 | 2 |
| #11725570 | 2 |
| #11725567 | 2 |
| #12349 | 7 |