Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
494 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 494 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×#1831 | C2 | semidirect |
| 3. #11727143 | C2 | semidirect |
| 4. #11725286 | C2 | semidirect |
| 56. #1831 | D7 | semidirect |
| 330. C7 | #7618 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#6438 | 2 |
| C7×#1831 | 2 |
| #11727143 | 2 |
| #11725286 | 2 |
| #11725285 | 2 |
| #7618 | 7 |