Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
444 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 444 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 |
|---|---|---|
| 3. C7×#1485 | C2 | semidirect |
| 4. #11729579 | C2 | semidirect |
| 6. #11725545 | C2 | semidirect |
| 7. #11725473 | C2 | semidirect |
| 79. #1485 | D7 | semidirect |
| 338. C7 | #9067 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11740779 | 2 |
| #11736734 | 2 |
| C7×#1485 | 2 |
| #11729579 | 2 |
| #11727613 | 2 |
| #11725545 | 2 |
| #11725473 | 2 |
| #9067 | 7 |