Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
218 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 218 conjugacy classes of subgroups — too many to draw. Only its 65 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. #11729139 | C2 | semidirect |
| 5. C7×#1365 | C2 | semidirect |
| 6. #11725370 | C2 | semidirect |
| 7. #11725276 | C2 | semidirect |
| 50. #1365 | D7 | semidirect |
| 73. C7⋊C16 | SD16 | semidirect |
| 188. C7 | #12453 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11729139 | 2 |
| #11729126 | 2 |
| #11727031 | 2 |
| #11726332 | 2 |
| C7×#1365 | 2 |
| #11725370 | 2 |
| #11725276 | 2 |
| #12453 | 7 |