Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
266 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 266 conjugacy classes of subgroups — too many to draw. Only its 71 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 |
|---|---|---|
| 239. C7 | #12413 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#3390 | 2 |
| #11729109 | 2 |
| #11728719 | 2 |
| #11728664 | 2 |
| #11725605 | 2 |
| #11725575 | 2 |
| #11725570 | 2 |
| #12413 | 7 |