Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
412 conjugacy classes of subgroups; only the 96 normal subgroups are shown.
This group has 412 conjugacy classes of subgroups — too many to draw. Only its 96 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. C4×C22⋊#595 | C2 | semidirect |
| 3. #11763687 | C2 | semidirect |
| 6. C22×C4×D17 | C4 | semidirect |
| 10. C2×C42×C17 | C4 | semidirect |
| 11. C2×#63227 | C4 | semidirect |
| 13. C2×C4⋊Dic17 | C4 | semidirect |
| 17. #10587539 | C4 | direct (N × H) |
| 36. C22⋊#595 | C2×C4 | semidirect |
| 50. C22×D17 | C42 | semidirect |
| 62. C2×C4×C17 | C42 | semidirect |
| 94. C4×C17 | #99 | semidirect |
| 118. C2×C42 | #595 | semidirect |
| 121. C17 | C4×#99 | semidirect |
| 175. C2×C4 | C4×#595 | semidirect |
| 199. C4 | #10587539 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10587539 | 2 |
| C4×C22⋊#595 | 2 |
| #11763687 | 2 |
| C2×C4×D68 | 2 |
| C4×#99 | 17 |