Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
4632 conjugacy classes of subgroups; only the 1106 normal subgroups are shown.
This group has 4632 conjugacy classes of subgroups — too many to draw. Only its 1106 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. C24×#595 | C2 | semidirect |
| 2. C22×C22⋊#595 | C2 | direct (N × H) |
| 4. C25×C17 | C4 | semidirect |
| 6. C24×D17 | C4 | semidirect |
| 7. C24×D17 | C4 | semidirect |
| 11. C23×#595 | C22 | semidirect |
| 12. C2×C22⋊#595 | C22 | direct (N × H) |
| 15. C24×C17 | C2×C4 | semidirect |
| 20. C23×D17 | C2×C4 | semidirect |
| 21. C23×D17 | C2×C4 | semidirect |
| 26. C22×#595 | C23 | semidirect |
| 27. C22⋊#595 | C23 | direct (N × H) |
| 29. C23×C17 | C22⋊C4 | semidirect |
| 31. C23×C17 | C22×C4 | semidirect |
| 35. C22×D17 | C22⋊C4 | semidirect |
| 37. C22×D17 | C22×C4 | semidirect |
| 38. C22×D17 | C22×C4 | semidirect |
| 43. C2×#595 | C24 | semidirect |
| 46. C22×C17 | C2×C22⋊C4 | semidirect |
| 48. C22×C17 | C23×C4 | semidirect |
| 52. C2×D17 | C2×C22⋊C4 | semidirect |
| 54. C2×D17 | C23×C4 | semidirect |
| 62. C2×C17 | C22×C22⋊C4 | semidirect |
| 65. D17 | C22×C22⋊C4 | semidirect |
| 72. C25 | #595 | semidirect |
| 76. C17 | C23×C22⋊C4 | semidirect |
| 88. C24 | C2×#595 | semidirect |
| 103. C23 | C22⋊#595 | direct (N × H) |
| 105. C23 | C22×#595 | semidirect |
| 117. C22 | C2×C22⋊#595 | direct (N × H) |
| 119. C22 | C23×#595 | semidirect |
| 125. C2 | C22×C22⋊#595 | 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 |
| C22×C22⋊#595 | 2 |
| C25×D17 | 2 |
| C23×C22⋊C4 | 17 |