Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
1880 conjugacy classes of subgroups; only the 634 normal subgroups are shown.
This group has 1880 conjugacy classes of subgroups — too many to draw. Only its 634 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. C2×(C2×#595)⋊C4 | C2 | direct (N × H) |
| 7. C23×#595 | C4 | semidirect |
| 9. C23×C4×C17 | C4 | semidirect |
| 10. C23×Dic17 | C4 | semidirect |
| 12. C22×C4×D17 | C4 | semidirect |
| 14. (C2×#595)⋊C4 | C22 | direct (N × H) |
| 25. C22×#595 | C2×C4 | semidirect |
| 28. C22×C4×C17 | C2×C4 | semidirect |
| 30. C22×Dic17 | C2×C4 | semidirect |
| 33. C2×C4×D17 | C2×C4 | semidirect |
| 53. C2×#595 | C22×C4 | semidirect |
| 55. C2×C4×C17 | C22×C4 | semidirect |
| 57. C2×Dic17 | C22×C4 | semidirect |
| 61. C22×C17 | #95 | semidirect |
| 66. C2×D17 | #95 | semidirect |
| 82. C2×C17 | C2×#95 | semidirect |
| 86. D17 | C2×#95 | semidirect |
| 98. C23×C4 | #595 | semidirect |
| 100. C17 | C22×#95 | semidirect |
| 120. C22×C4 | C2×#595 | semidirect |
| 145. C2×C4 | C22×#595 | semidirect |
| 156. C22 | (C2×#595)⋊C4 | direct (N × H) |
| 167. C2 | C2×(C2×#595)⋊C4 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C24×#595 | 2 |
| C2×(C2×#595)⋊C4 | 2 |
| C23×C4×D17 | 2 |
| C22×#95 | 17 |