Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
464 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 464 conjugacy classes of subgroups — too many to draw. Only its 81 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. #11729451 | C2 | semidirect |
| 3. #11729445 | C2 | semidirect |
| 6. #11727738 | C2 | semidirect |
| 7. #11725490 | C2 | semidirect |
| 394. C7 | #10562 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#3193 | 2 |
| #11729451 | 2 |
| #11729445 | 2 |
| #11729437 | 2 |
| #11729429 | 2 |
| #11727738 | 2 |
| #11725490 | 2 |
| #10562 | 7 |