Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
310 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 310 conjugacy classes of subgroups — too many to draw. Only its 131 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 |
|---|---|---|
| 15. #89307 | C4 | semidirect |
| 175. C7 | #12596 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#89307 | 2 |
| #11727503 | 2 |
| C7×#1376 | 2 |
| #11725618 | 2 |
| #11725464 | 2 |
| #12596 | 7 |