Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
346 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 346 conjugacy classes of subgroups — too many to draw. Only its 67 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. #11737059 | C2 | semidirect |
| 2. C7×#2206 | C2 | semidirect |
| 3. #11729042 | C2 | semidirect |
| 4. #11729036 | C2 | semidirect |
| 5. #11725569 | C2 | semidirect |
| 6. #11725370 | C2 | semidirect |
| 7. #11725362 | C2 | semidirect |
| 56. #2206 | D7 | semidirect |
| 133. D28 | D16 | semidirect |
| 262. C7 | #12340 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11737059 | 2 |
| C7×#2206 | 2 |
| #11729042 | 2 |
| #11729036 | 2 |
| #11725569 | 2 |
| #11725370 | 2 |
| #11725362 | 2 |
| #12340 | 7 |