Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
310 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 310 conjugacy classes of subgroups — too many to draw. Only its 113 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 |
|---|---|---|
| 20. #89306 | C4 | semidirect |
| 214. C7 | #13186 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#89308 | 2 |
| C2×#89306 | 2 |
| #11728413 | 2 |
| #11728308 | 2 |
| C2×#89282 | 2 |
| C7×#1386 | 2 |
| #11725532 | 2 |
| #13186 | 7 |