Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
344 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 344 conjugacy classes of subgroups — too many to draw. Only its 85 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 |
|---|---|---|
| 275. C7 | #10495 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#3230 | 2 |
| #11729588 | 2 |
| #11729579 | 2 |
| #11729544 | 2 |
| #11729527 | 2 |
| #11728502 | 2 |
| #11725549 | 2 |
| #10495 | 7 |