Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
2528 conjugacy classes of subgroups; only the 850 normal subgroups are shown.
This group has 2528 conjugacy classes of subgroups — too many to draw. Only its 850 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. C2×D4×#595 | C2 | direct (N × H) |
| 3. C22×C4⋊#595 | C2 | semidirect |
| 4. C22×C22⋊#595 | C2 | semidirect |
| 5. C22×C4×#595 | C2 | semidirect |
| 12. C23×#595 | C22 | semidirect |
| 13. C22×D4×C17 | C4 | semidirect |
| 14. C22×C22⋊D17 | C4 | semidirect |
| 15. C2×D4×D17 | C4 | semidirect |
| 17. C22×D68 | C4 | semidirect |
| 19. C2×C22⋊#595 | C22 | semidirect |
| 20. D4×#595 | C22 | direct (N × H) |
| 21. C2×C4⋊#595 | C22 | semidirect |
| 22. C2×C4×#595 | C22 | semidirect |
| 23. C24×C17 | C2×C4 | semidirect |
| 26. C23×D17 | C2×C4 | semidirect |
| 27. C23×D17 | C2×C4 | semidirect |
| 33. C22×#595 | D4 | direct (N × H) |
| 37. C22×#595 | C23 | semidirect |
| 38. C2×D4×C17 | C2×C4 | semidirect |
| 39. C22×C4×C17 | C2×C4 | semidirect |
| 40. C2×C22⋊D17 | C2×C4 | semidirect |
| 41. C22×Dic17 | C2×C4 | semidirect |
| 42. D4×D17 | C2×C4 | semidirect |
| 44. C2×D68 | C2×C4 | semidirect |
| 45. C2×C4×D17 | C2×C4 | semidirect |
| 47. C22⋊#595 | C23 | semidirect |
| 48. C4⋊#595 | C23 | semidirect |
| 49. C4×#595 | C23 | semidirect |
| 52. C23×C17 | C22×C4 | semidirect |
| 58. C22×D17 | C22×C4 | semidirect |
| 59. C22×D17 | C22×C4 | semidirect |
| 67. C2×#595 | C2×D4 | direct (N × H) |
| 71. D4×C17 | C22×C4 | semidirect |
| 72. C2×C4×C17 | C22×C4 | semidirect |
| 73. C22⋊D17 | C22×C4 | semidirect |
| 74. C2×Dic17 | C22×C4 | semidirect |
| 75. D68 | C22×C4 | semidirect |
| 76. C4×D17 | C22×C4 | semidirect |
| 80. C22×C17 | C4×D4 | semidirect |
| 82. C22×C17 | C23×C4 | semidirect |
| 87. C2×D17 | C4×D4 | semidirect |
| 89. C2×D17 | C23×C4 | semidirect |
| 95. #595 | C22×D4 | direct (N × H) |
| 96. C4×C17 | C23×C4 | semidirect |
| 97. Dic17 | C23×C4 | semidirect |
| 105. C2×C17 | C2×C4×D4 | semidirect |
| 108. D17 | C2×C4×D4 | semidirect |
| 116. C22×D4 | #595 | direct (N × H) |
| 127. C17 | C22×C4×D4 | semidirect |
| 134. C24 | C2×#595 | semidirect |
| 139. C2×D4 | C2×#595 | direct (N × H) |
| 151. C22×C4 | C2×#595 | semidirect |
| 168. C23 | C22×#595 | semidirect |
| 171. D4 | C22×#595 | direct (N × H) |
| 182. C2×C4 | C22×#595 | semidirect |
| 194. C22 | D4×#595 | direct (N × H) |
| 196. C22 | C23×#595 | semidirect |
| 201. C4 | C23×#595 | semidirect |
| 207. C2 | C2×D4×#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 |
| C2×D4×#595 | 2 |
| C22×C4⋊#595 | 2 |
| C22×C22⋊#595 | 2 |
| C22×C4×#595 | 2 |
| C22×D4×D17 | 2 |
| C22×C4×D4 | 17 |