Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
490 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 490 conjugacy classes of subgroups — too many to draw. Only its 123 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. #11741225 | C2 | semidirect |
| 3. C7×#1812 | C2 | semidirect |
| 4. #11728406 | C2 | semidirect |
| 5. #11725531 | C2 | semidirect |
| 12. #89907 | C4 | semidirect |
| 49. C2×C7⋊C16 | D4 | semidirect |
| 53. #1812 | D7 | semidirect |
| 233. C7 | #13074 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11741244 | 2 |
| #11741225 | 2 |
| C7×#1812 | 2 |
| #11728406 | 2 |
| #11725531 | 2 |
| #13074 | 7 |