Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
470 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 470 conjugacy classes of subgroups — too many to draw. Only its 79 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. C2×#89343 | C2 | semidirect |
| 3. #11729531 | C2 | semidirect |
| 4. #11725579 | C2 | semidirect |
| 17. #89343 | C22 | semidirect |
| 19. #89341 | C22 | semidirect |
| 314. C7 | #13573 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C7×#456 | 2 |
| C2×#89343 | 2 |
| #11729531 | 2 |
| #11725579 | 2 |
| #13573 | 7 |