Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
212 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 212 conjugacy classes of subgroups — too many to draw. Only its 69 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 |
|---|---|---|
| 1. C7×#1593 | C2 | semidirect |
| 4. #11725570 | C2 | semidirect |
| 6. #11725270 | C2 | semidirect |
| 7. #11725248 | C2 | semidirect |
| 47. #1593 | D7 | semidirect |
| 74. C7⋊C16 | M16 | semidirect |
| 189. C7 | #12087 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#1593 | 2 |
| #11728667 | 2 |
| #11725837 | 2 |
| #11725570 | 2 |
| #11725271 | 2 |
| #11725270 | 2 |
| #11725248 | 2 |
| #12087 | 7 |