Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
428 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 428 conjugacy classes of subgroups — too many to draw. Only its 93 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 |
|---|---|---|
| 2. C7×#2159 | C2 | semidirect |
| 3. C2×#89311 | C2 | semidirect |
| 4. C2×#89310 | C2 | semidirect |
| 5. #11728400 | C2 | semidirect |
| 6. C2×#89286 | C2 | semidirect |
| 7. #11725530 | C2 | semidirect |
| 53. C7×M32 | D4 | semidirect |
| 70. #2159 | D7 | semidirect |
| 207. M32 | D28 | semidirect |
| 338. C7 | #13387 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11736628 | 2 |
| C7×#2159 | 2 |
| C2×#89311 | 2 |
| C2×#89310 | 2 |
| #11728400 | 2 |
| C2×#89286 | 2 |
| #11725530 | 2 |
| #13387 | 7 |