Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
450 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 450 conjugacy classes of subgroups — too many to draw. Only its 111 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. C7×#1568 | C2 | semidirect |
| 4. #11727486 | C2 | semidirect |
| 5. #11725561 | C2 | semidirect |
| 54. #1568 | D7 | semidirect |
| 248. C7 | #8620 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C8×D28 | 2 |
| C7×#1568 | 2 |
| #11728581 | 2 |
| #11727486 | 2 |
| #11725561 | 2 |
| #8620 | 7 |