Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
398 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 398 conjugacy classes of subgroups — too many to draw. Only its 103 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. #11725816 | C2 | semidirect |
| 4. C8×C7⋊C16 | C2 | semidirect |
| 25. #1712 | D7 | semidirect |
| 38. C7⋊C16 | D8 | semidirect |
| 54. C7×C8 | D16 | semidirect |
| 97. C8 | #6400 | semidirect |
| 99. C7 | #12515 | 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 |
| #11725816 | 2 |
| C8×C7⋊C16 | 2 |
| #12515 | 7 |