Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
424 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 424 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. #11729588 | C2 | semidirect |
| 3. #11729579 | C2 | semidirect |
| 6. #11728502 | C2 | semidirect |
| 7. #11725549 | C2 | semidirect |
| 305. C7 | #10492 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#3208 | 2 |
| #11729588 | 2 |
| #11729579 | 2 |
| #11729520 | 2 |
| #11729513 | 2 |
| #11728502 | 2 |
| #11725549 | 2 |
| #10492 | 7 |