Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
608 conjugacy classes of subgroups; only the 170 normal subgroups are shown.
This group has 608 conjugacy classes of subgroups — too many to draw. Only its 170 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. C2×D4×#595 | C2 | semidirect |
| 2. #11763850 | C2 | direct (N × H) |
| 3. C2×#10587533 | C2 | semidirect |
| 4. C2×#10587547 | C2 | semidirect |
| 5. C2×#10587532 | C2 | semidirect |
| 11. D4×#595 | C22 | semidirect |
| 15. C2×D8×C17 | C4 | semidirect |
| 16. C2×#63228 | C4 | semidirect |
| 17. D8×D17 | C4 | semidirect |
| 19. C2×D136 | C4 | semidirect |
| 21. #10587547 | C22 | semidirect |
| 22. #10587533 | C22 | semidirect |
| 23. #10587532 | C22 | semidirect |
| 29. C2×D4×C17 | C2×C4 | semidirect |
| 33. D4×D17 | C2×C4 | semidirect |
| 35. C2×D68 | C2×C4 | semidirect |
| 45. D8×C17 | C2×C4 | semidirect |
| 46. C2×C8×C17 | C2×C4 | semidirect |
| 47. #63228 | C2×C4 | semidirect |
| 48. C2×#3622 | C2×C4 | semidirect |
| 49. D136 | C2×C4 | semidirect |
| 50. C8×D17 | C2×C4 | semidirect |
| 65. D4×C17 | C22×C4 | semidirect |
| 71. D68 | C22×C4 | semidirect |
| 77. C8×C17 | C22×C4 | semidirect |
| 78. #3622 | C22×C4 | semidirect |
| 104. C2×C17 | #442 | semidirect |
| 107. D17 | #442 | semidirect |
| 115. C2×D8 | #595 | semidirect |
| 126. C17 | C2×#442 | semidirect |
| 134. C2×D4 | C2×#595 | semidirect |
| 142. D8 | C2×#595 | semidirect |
| 149. C2×C8 | C2×#595 | semidirect |
| 167. D4 | C22×#595 | semidirect |
| 181. C8 | C22×#595 | semidirect |
| 203. C2 | #11763850 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D4×#595 | 2 |
| #11763850 | 2 |
| C2×#10587533 | 2 |
| C2×#10587547 | 2 |
| C2×#10587532 | 2 |
| C2×D8×D17 | 2 |
| C2×#442 | 17 |