Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
290 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 290 conjugacy classes of subgroups — too many to draw. Only its 59 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 |
|---|---|---|
| 5. C7×#423 | C4 | semidirect |
| 8. C43×C7 | C4 | semidirect |
| 11. #89343 | C4 | semidirect |
| 12. #89340 | C4 | semidirect |
| 75. #423 | Dic7 | semidirect |
| 80. C43 | Dic7 | semidirect |
| 217. C7 | #7497 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#1962 | 2 |
| #11729574 | 2 |
| #11729573 | 2 |
| #7497 | 7 |