Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
438 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 438 conjugacy classes of subgroups — too many to draw. Only its 85 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 |
|---|---|---|
| 2. #11736782 | C2 | semidirect |
| 3. #11728562 | C2 | semidirect |
| 4. #11728538 | C2 | semidirect |
| 5. #11728529 | C2 | semidirect |
| 6. C7×#1287 | C2 | semidirect |
| 7. C7⋊#1308 | C2 | semidirect |
| 73. #1287 | D7 | semidirect |
| 305. C7 | #9333 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11736794 | 2 |
| #11736782 | 2 |
| #11728562 | 2 |
| #11728538 | 2 |
| #11728529 | 2 |
| C7×#1287 | 2 |
| C7⋊#1308 | 2 |
| #9333 | 7 |