Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
334 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 334 conjugacy classes of subgroups — too many to draw. Only its 89 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×#1571 | C2 | semidirect |
| 4. #11728247 | C2 | semidirect |
| 5. #11728198 | C2 | semidirect |
| 7. #11725543 | C2 | semidirect |
| 52. #1571 | D7 | semidirect |
| 235. C7 | #10665 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#1571 | 2 |
| #11728512 | 2 |
| #11728267 | 2 |
| #11728247 | 2 |
| #11728198 | 2 |
| #11728180 | 2 |
| #11725543 | 2 |
| #10665 | 7 |