Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
442 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 442 conjugacy classes of subgroups — too many to draw. Only its 99 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×#2981 | C2 | semidirect |
| 3. #11729561 | C2 | semidirect |
| 4. #11728565 | C2 | semidirect |
| 5. #11728512 | C2 | semidirect |
| 6. #11725561 | C2 | semidirect |
| 7. #11725553 | C2 | semidirect |
| 72. #2981 | D7 | semidirect |
| 321. C7 | #9371 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#2981 | 2 |
| #11740752 | 2 |
| #11729561 | 2 |
| #11728565 | 2 |
| #11728512 | 2 |
| #11725561 | 2 |
| #11725553 | 2 |
| #9371 | 7 |