Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
360 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 360 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 |
|---|---|---|
| 260. C7 | #9336 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#3236 | 2 |
| #11740778 | 2 |
| #11729586 | 2 |
| #11729491 | 2 |
| #11729490 | 2 |
| C7⋊#1308 | 2 |
| #11725563 | 2 |
| #9336 | 7 |