Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
492 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 492 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. #11740673 | C2 | semidirect |
| 3. C7×#1548 | C2 | semidirect |
| 6. #11725543 | C2 | semidirect |
| 7. #11725519 | C2 | semidirect |
| 16. #89857 | C4 | semidirect |
| 18. #89853 | C4 | semidirect |
| 71. #1548 | D7 | semidirect |
| 119. C4×Dic7 | SD16 | semidirect |
| 337. C7 | #9301 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11740673 | 2 |
| #11740658 | 2 |
| C7×#1548 | 2 |
| #11728544 | 2 |
| #11728267 | 2 |
| #11725543 | 2 |
| #11725519 | 2 |
| #9301 | 7 |