Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
444 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 444 conjugacy classes of subgroups — too many to draw. Only its 99 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×#2381 | C2 | semidirect |
| 3. #11729530 | C2 | semidirect |
| 6. #11725439 | C2 | semidirect |
| 7. #11725439 | C2 | semidirect |
| 15. #89865 | C4 | semidirect |
| 17. #89860 | C4 | semidirect |
| 63. #2381 | D7 | semidirect |
| 278. C7 | #9430 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#2381 | 2 |
| #11740644 | 2 |
| #11729530 | 2 |
| #11727318 | 2 |
| #11725439 | 2 |
| #9430 | 7 |