Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
380 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 66 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. #11763876 | C2 | semidirect |
| 2. C2×#10587539 | C2 | semidirect |
| 3. D17⋊#99 | C2 | semidirect |
| 4. #11763686 | C2 | semidirect |
| 13. C17×#123 | C4 | semidirect |
| 14. #10587623 | C4 | semidirect |
| 15. #10587615 | C4 | semidirect |
| 20. #10587568 | C4 | semidirect |
| 25. C23×D17 | C2×C4 | semidirect |
| 32. C22×C4×C17 | C2×C4 | semidirect |
| 50. C22⋊#595 | D4 | semidirect |
| 55. C22⋊C4×C17 | C2×C4 | semidirect |
| 56. C22⋊Dic17 | C2×C4 | semidirect |
| 145. #123 | #595 | semidirect |
| 160. C17 | #1913 | semidirect |
| 181. C22×C4 | C2×#595 | semidirect |
| 196. C22⋊C4 | C2×#595 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11763876 | 2 |
| C2×#10587539 | 2 |
| D17⋊#99 | 2 |
| #11763686 | 2 |
| #11763370 | 2 |
| #1913 | 17 |