Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
472 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 472 conjugacy classes of subgroups — too many to draw. Only its 103 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×#2971 | C2 | semidirect |
| 3. #11729394 | C2 | semidirect |
| 4. #11728582 | C2 | semidirect |
| 5. #11727614 | C2 | semidirect |
| 6. #11725564 | C2 | semidirect |
| 7. #11725475 | C2 | semidirect |
| 85. #2971 | D7 | semidirect |
| 386. C7 | #9350 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#2971 | 2 |
| #11739972 | 2 |
| #11729394 | 2 |
| #11728582 | 2 |
| #11727614 | 2 |
| #11725564 | 2 |
| #11725475 | 2 |
| #9350 | 7 |