Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
1774 conjugacy classes of subgroups; only the 667 normal subgroups are shown.
This group has 1774 conjugacy classes of subgroups — too many to draw. Only its 667 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 |
|---|---|---|
| 7. C7×#376 | C4 | semidirect |
| 37. C42×C7 | C4⋊C4 | semidirect |
| 44. #376 | Dic7 | semidirect |
| 94. C42 | C4⋊Dic7 | semidirect |
| 113. C7 | #13856 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C7×#376 | 2 |
| C2×C4×C4⋊Dic7 | 2 |
| #11727173 | 2 |
| #13856 | 7 |