Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
276 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 276 conjugacy classes of subgroups — too many to draw. Only its 83 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 |
|---|---|---|
| 240. C7 | #10613 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#1548 | 2 |
| #11729529 | 2 |
| #11729527 | 2 |
| #11728507 | 2 |
| #11728502 | 2 |
| #11728249 | 2 |
| C7⋊#1309 | 2 |
| #10613 | 7 |