Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
404 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 404 conjugacy classes of subgroups — too many to draw. Only its 109 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 |
|---|---|---|
| 4. #11728245 | C2 | semidirect |
| 5. #11728244 | C2 | semidirect |
| 6. C7⋊#1309 | C2 | semidirect |
| 7. C7⋊#1309 | C2 | semidirect |
| 290. C7 | #8640 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11740720 | 2 |
| C7×#1560 | 2 |
| #11729564 | 2 |
| #11728245 | 2 |
| #11728244 | 2 |
| C7⋊#1309 | 2 |
| #8640 | 7 |