Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
950 conjugacy classes of subgroups; only the 143 normal subgroups are shown.
This group has 950 conjugacy classes of subgroups — too many to draw. Only its 143 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 |
|---|---|---|
| 2. C7×#1984 | C2 | semidirect |
| 3. #11729391 | C2 | semidirect |
| 4. #11728186 | C2 | semidirect |
| 5. #11727489 | C2 | semidirect |
| 65. #1984 | D7 | semidirect |
| 323. C7 | #8354 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11742886 | 2 |
| C7×#1984 | 2 |
| #11729391 | 2 |
| #11728186 | 2 |
| #11727489 | 2 |
| #8354 | 7 |