Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
350 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 350 conjugacy classes of subgroups — too many to draw. Only its 95 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 |
|---|---|---|
| 180. C7 | #10586 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11731664 | 2 |
| C7×#1836 | 2 |
| #11727329 | 2 |
| #11725465 | 2 |
| #11725436 | 2 |
| #10586 | 7 |