Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
672 conjugacy classes of subgroups; only the 162 normal subgroups are shown.
This group has 672 conjugacy classes of subgroups — too many to draw. Only its 162 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. #11763759 | C2 | semidirect |
| 2. #11763751 | C2 | semidirect |
| 4. C4×C22⋊#595 | C2 | semidirect |
| 12. C2×C4⋊#595 | C22 | semidirect |
| 13. C2×C4×#595 | C22 | semidirect |
| 14. C2×C22⋊C4×C17 | C4 | semidirect |
| 15. C2×C22⋊Dic17 | C4 | semidirect |
| 16. C2×#63227 | C4 | semidirect |
| 17. C2×#63227 | C4 | semidirect |
| 18. C22⋊C4×D17 | C4 | semidirect |
| 20. (C2×#595)⋊C4 | C22 | semidirect |
| 21. (C2×#595)⋊C4 | C22 | semidirect |
| 138. C2×C22⋊C4 | #595 | semidirect |
| 142. C17 | #2312 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11763759 | 2 |
| #11763751 | 2 |
| #11763750 | 2 |
| C4×C22⋊#595 | 2 |
| C2×C22⋊C4×D17 | 2 |
| #2312 | 17 |