Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
680 conjugacy classes of subgroups; only the 138 normal subgroups are shown.
This group has 680 conjugacy classes of subgroups — too many to draw. Only its 138 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. #11763687 | C2 | semidirect |
| 6. C22×C4×D17 | C4 | semidirect |
| 9. C2×C22⋊#595 | C4 | semidirect |
| 11. C2×C22⋊C4×C17 | C4 | semidirect |
| 12. C2×C22⋊Dic17 | C4 | semidirect |
| 28. C22×C4×C17 | C2×C4 | semidirect |
| 29. C22×Dic17 | C2×C4 | semidirect |
| 35. C22⋊#595 | C2×C4 | semidirect |
| 111. D17 | #342 | semidirect |
| 123. C2×C22⋊C4 | #595 | semidirect |
| 124. C17 | C2×#342 | semidirect |
| 141. C22×C4 | C2×#595 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C22⋊#595 | 2 |
| #11763687 | 2 |
| C2×C22⋊C4×D17 | 2 |
| C2×#342 | 17 |