Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
412 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 412 conjugacy classes of subgroups — too many to draw. Only its 90 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 |
|---|---|---|
| 3. C22⋊C4×#595 | C2 | semidirect |
| 4. #11763686 | C2 | semidirect |
| 6. C23×#595 | C4 | semidirect |
| 9. C2×C22⋊#595 | C4 | semidirect |
| 14. C2×C4⋊#595 | C4 | semidirect |
| 16. C2×C4×#595 | C4 | semidirect |
| 18. #10587551 | C4 | semidirect |
| 20. #10587539 | C4 | semidirect |
| 21. C17×#99 | C4 | semidirect |
| 22. #10587505 | C4 | semidirect |
| 23. #10587477 | C4 | semidirect |
| 48. C22⋊#595 | C2×C4 | semidirect |
| 53. C22⋊C4×C17 | C2×C4 | semidirect |
| 54. C22⋊Dic17 | C2×C4 | semidirect |
| 56. C23×C17 | C42 | semidirect |
| 64. C22×D17 | C42 | semidirect |
| 87. C2×C4×C17 | C42 | semidirect |
| 91. C2×Dic17 | C42 | semidirect |
| 122. #595 | #99 | direct (N × H) |
| 157. #99 | #595 | direct (N × H) |
| 159. C17 | C4×#99 | semidirect |
| 188. C22⋊C4 | C2×#595 | semidirect |
| 203. C23 | C4×#595 | semidirect |
| 232. C2×C4 | C4×#595 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D4×#595 | 2 |
| D17⋊#99 | 2 |
| C22⋊C4×#595 | 2 |
| #11763686 | 2 |
| #99×D17 | 2 |
| C4×#99 | 17 |