Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
1112 conjugacy classes of subgroups; only the 218 normal subgroups are shown.
This group has 1112 conjugacy classes of subgroups — too many to draw. Only its 218 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. C22×C22⋊#595 | C2 | semidirect |
| 2. C2×#10587539 | C2 | direct (N × H) |
| 4. C24×D17 | C4 | semidirect |
| 7. C23×C4×C17 | C4 | semidirect |
| 10. C22×D68 | C4 | semidirect |
| 13. C2×C22⋊#595 | C22 | semidirect |
| 14. #10587539 | C22 | direct (N × H) |
| 21. C23×D17 | C2×C4 | semidirect |
| 29. C22×C4×C17 | C2×C4 | semidirect |
| 34. C2×D68 | C2×C4 | semidirect |
| 37. C22⋊#595 | C23 | semidirect |
| 54. C22×D17 | C22×C4 | semidirect |
| 62. C2×C4×C17 | C22×C4 | semidirect |
| 68. C22×C17 | #99 | semidirect |
| 91. C2×C17 | C2×#99 | semidirect |
| 103. C23×C4 | #595 | semidirect |
| 107. C17 | C22×#99 | semidirect |
| 128. C22×C4 | C2×#595 | semidirect |
| 157. C2×C4 | C22×#595 | semidirect |
| 172. C22 | #10587539 | direct (N × H) |
| 183. C2 | C2×#10587539 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C22⋊#595 | 2 |
| C2×#10587539 | 2 |
| C23×D68 | 2 |
| C22×#99 | 17 |