Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
2488 conjugacy classes of subgroups; only the 1106 normal subgroups are shown.
This group has 2488 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 |
|---|---|---|
| 2. C22×C4⋊#595 | C2 | direct (N × H) |
| 7. C23×C4×C17 | C4 | semidirect |
| 8. C23×Dic17 | C4 | semidirect |
| 9. C22×C4×D17 | C4 | semidirect |
| 11. C2×C4⋊#595 | C22 | direct (N × H) |
| 19. C22×C4×C17 | C2×C4 | semidirect |
| 20. C22×Dic17 | C2×C4 | semidirect |
| 21. C2×C4×D17 | C2×C4 | semidirect |
| 23. C4⋊#595 | C23 | direct (N × H) |
| 24. C23×C17 | C4⋊C4 | semidirect |
| 26. C22×D17 | C4⋊C4 | semidirect |
| 33. C2×C4×C17 | C22×C4 | semidirect |
| 34. C2×Dic17 | C22×C4 | semidirect |
| 35. C4×D17 | C22×C4 | semidirect |
| 38. C22×C17 | C2×C4⋊C4 | semidirect |
| 40. C2×D17 | C2×C4⋊C4 | semidirect |
| 46. C4×C17 | C23×C4 | semidirect |
| 47. Dic17 | C23×C4 | semidirect |
| 51. C2×C17 | C22×C4⋊C4 | semidirect |
| 53. D17 | C22×C4⋊C4 | semidirect |
| 62. C23×C4 | #595 | semidirect |
| 64. C17 | C23×C4⋊C4 | semidirect |
| 75. C22×C4 | C2×#595 | semidirect |
| 82. C23 | C4⋊#595 | direct (N × H) |
| 89. C2×C4 | C22×#595 | semidirect |
| 95. C22 | C2×C4⋊#595 | direct (N × H) |
| 99. C4 | C23×#595 | semidirect |
| 103. C2 | C22×C4⋊#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×C4⋊#595 | 2 |
| C23×C4×D17 | 2 |
| C23×C4⋊C4 | 17 |