Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
400 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 400 conjugacy classes of subgroups — too many to draw. Only its 99 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 |
|---|---|---|
| 315. C7 | #9725 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11740789 | 2 |
| C7×#1485 | 2 |
| #11729575 | 2 |
| #11728523 | 2 |
| #11728493 | 2 |
| C4×#6396 | 2 |
| #11727616 | 2 |
| #9725 | 7 |