Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
518 conjugacy classes of subgroups; only the 291 normal subgroups are shown.
This group has 518 conjugacy classes of subgroups — too many to draw. Only its 291 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 |
|---|---|---|
| 12. C7×#322 | C4 | semidirect |
| 14. #89250 | C4 | semidirect |
| 15. C8×C7⋊C8 | C4 | semidirect |
| 61. #322 | Dic7 | semidirect |
| 131. C7 | #7844 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C7×#322 | 2 |
| #11727504 | 2 |
| C4×#6389 | 2 |
| C2×#89250 | 2 |
| C2×C8×C7⋊C8 | 2 |
| #7844 | 7 |