Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
318 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 318 conjugacy classes of subgroups — too many to draw. Only its 93 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 |
|---|---|---|
| 257. C7 | #13479 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#2141 | 2 |
| #11729820 | 2 |
| C2×#89360 | 2 |
| C2×#89306 | 2 |
| #11728416 | 2 |
| #11728403 | 2 |
| #11725623 | 2 |
| #13479 | 7 |