Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
218 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 218 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×#2254 | C2 | semidirect |
| 5. #11725608 | C2 | semidirect |
| 6. #11725607 | C2 | semidirect |
| 7. #11725307 | C2 | semidirect |
| 45. #2254 | D7 | semidirect |
| 72. C7×C16 | SD16 | semidirect |
| 163. C16 | #1143 | semidirect |
| 188. C7 | #12453 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#2254 | 2 |
| #11729126 | 2 |
| #11729125 | 2 |
| C16×D28 | 2 |
| #11725608 | 2 |
| #11725607 | 2 |
| #11725307 | 2 |
| #12453 | 7 |