Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
508 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 508 conjugacy classes of subgroups — too many to draw. Only its 113 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. #11740672 | C2 | semidirect |
| 3. C7×#1546 | C2 | semidirect |
| 6. #11725543 | C2 | semidirect |
| 7. #11725519 | C2 | semidirect |
| 16. #89860 | C4 | semidirect |
| 18. #89850 | C4 | semidirect |
| 72. #1546 | D7 | semidirect |
| 347. C7 | #9300 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11740672 | 2 |
| #11740660 | 2 |
| C7×#1546 | 2 |
| #11728544 | 2 |
| #11728267 | 2 |
| #11725543 | 2 |
| #11725519 | 2 |
| #9300 | 7 |