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×#10587551 | C2 | direct (N × H) |
| 4. C25×C17 | C4 | semidirect |
| 9. C22×C22⋊D17 | C4 | semidirect |
| 11. C23×Dic17 | C4 | semidirect |
| 13. C2×C22⋊#595 | C22 | semidirect |
| 14. #10587551 | C22 | direct (N × H) |
| 19. C24×C17 | C2×C4 | semidirect |
| 31. C2×C22⋊D17 | C2×C4 | semidirect |
| 35. C22×Dic17 | C2×C4 | semidirect |
| 37. C22⋊#595 | C23 | semidirect |
| 47. C23×C17 | C22×C4 | semidirect |
| 64. C2×Dic17 | C22×C4 | semidirect |
| 72. C22×C17 | #99 | semidirect |
| 92. C2×C17 | C2×#99 | semidirect |
| 97. C25 | #595 | semidirect |
| 107. C17 | C22×#99 | semidirect |
| 117. C24 | C2×#595 | semidirect |
| 150. C23 | C22×#595 | semidirect |
| 172. C22 | #10587551 | direct (N × H) |
| 183. C2 | C2×#10587551 | 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×#10587551 | 2 |
| C23×C22⋊D17 | 2 |
| C22×#99 | 17 |