Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
582 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 582 conjugacy classes of subgroups — too many to draw. Only its 103 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. C7×#2973 | C2 | semidirect |
| 3. C4×#6408 | C2 | semidirect |
| 4. #11727731 | C2 | semidirect |
| 5. #11725488 | C2 | semidirect |
| 17. #89763 | C4 | semidirect |
| 18. #89758 | C4 | semidirect |
| 19. #89732 | C4 | semidirect |
| 21. #89721 | C4 | semidirect |
| 55. C7×C22⋊C8 | D4 | semidirect |
| 64. #2973 | D7 | semidirect |
| 218. C22⋊C8 | C22⋊D7 | semidirect |
| 366. C7 | #9185 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#2973 | 2 |
| #11739867 | 2 |
| C4×#6408 | 2 |
| #11727731 | 2 |
| #11725488 | 2 |
| #9185 | 7 |