Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
234 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 234 conjugacy classes of subgroups — too many to draw. Only its 71 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×#1713 | C2 | semidirect |
| 4. #11725608 | C2 | semidirect |
| 5. #11725246 | C2 | semidirect |
| 36. #1713 | D7 | semidirect |
| 56. D56 | Q16 | semidirect |
| 157. C7 | #12447 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#1713 | 2 |
| #11729142 | 2 |
| C8×D56 | 2 |
| #11725608 | 2 |
| #11725246 | 2 |
| #12447 | 7 |