Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
340 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 340 conjugacy classes of subgroups — too many to draw. Only its 87 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×#1712 | C2 | semidirect |
| 2. #11729044 | C2 | semidirect |
| 3. #11729042 | C2 | semidirect |
| 4. #11725812 | C2 | semidirect |
| 5. #11725244 | C2 | semidirect |
| 36. #1712 | D7 | semidirect |
| 85. C7×C8 | D16 | semidirect |
| 154. C8 | #6400 | semidirect |
| 156. C7 | #12525 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#1712 | 2 |
| #11729044 | 2 |
| #11729042 | 2 |
| #11725812 | 2 |
| #11725244 | 2 |
| #12525 | 7 |