Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
542 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 542 conjugacy classes of subgroups — too many to draw. Only its 105 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. #11730753 | C2 | semidirect |
| 4. #11728534 | C2 | semidirect |
| 5. #11728532 | C2 | semidirect |
| 7. C7×#1276 | C2 | semidirect |
| 77. #1276 | D7 | semidirect |
| 323. C7 | #10286 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11736714 | 2 |
| #11736713 | 2 |
| #11730753 | 2 |
| #11728534 | 2 |
| #11728532 | 2 |
| #11727149 | 2 |
| C7×#1276 | 2 |
| #10286 | 7 |