Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
540 conjugacy classes of subgroups; only the 162 normal subgroups are shown.
This group has 540 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 |
|---|---|---|
| 2. #11763760 | C2 | semidirect |
| 3. #11763759 | C2 | semidirect |
| 4. #11763752 | C2 | semidirect |
| 5. #11763751 | C2 | semidirect |
| 6. C4×C4⋊#595 | C2 | semidirect |
| 7. #11763745 | C2 | semidirect |
| 17. C4×D4×C17 | C4 | semidirect |
| 18. D4×Dic17 | C4 | semidirect |
| 19. C4×C22⋊D17 | C4 | semidirect |
| 20. #10587579 | C4 | semidirect |
| 22. #10587567 | C4 | semidirect |
| 24. C4×D68 | C4 | semidirect |
| 148. C4×D4 | #595 | semidirect |
| 163. C17 | #2319 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11763761 | 2 |
| #11763760 | 2 |
| #11763759 | 2 |
| #11763752 | 2 |
| #11763751 | 2 |
| C4×C4⋊#595 | 2 |
| #11763745 | 2 |
| C4×D4×D17 | 2 |
| #2319 | 17 |