Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
314 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 314 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. #11737187 | C2 | semidirect |
| 2. C7×#2207 | C2 | semidirect |
| 3. #11729042 | C2 | semidirect |
| 5. #11725571 | C2 | semidirect |
| 6. #11725371 | C2 | semidirect |
| 7. #11725362 | C2 | semidirect |
| 56. #2207 | D7 | semidirect |
| 128. D28 | SD32 | semidirect |
| 247. C7 | #12342 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11737187 | 2 |
| C7×#2207 | 2 |
| #11729042 | 2 |
| #11729036 | 2 |
| #11725571 | 2 |
| #11725371 | 2 |
| #11725362 | 2 |
| #12342 | 7 |