Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
826 conjugacy classes of subgroups; only the 203 normal subgroups are shown.
This group has 826 conjugacy classes of subgroups — too many to draw. Only its 203 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. #11736487 | C2 | semidirect |
| 3. C7×#1838 | C2 | semidirect |
| 4. #11728266 | C2 | semidirect |
| 5. #11727559 | C2 | semidirect |
| 6. #11726700 | C2 | semidirect |
| 17. #89487 | C4 | semidirect |
| 18. #89484 | C4 | semidirect |
| 50. #1838 | D7 | semidirect |
| 198. C7 | #22283 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11736487 | 2 |
| #11735944 | 2 |
| C7×#1838 | 2 |
| #11728266 | 2 |
| #11727559 | 2 |
| #11726700 | 2 |
| #22283 | 7 |