Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
528 conjugacy classes of subgroups; only the 160 normal subgroups are shown.
This group has 528 conjugacy classes of subgroups — too many to draw. Only its 160 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. #11763876 | C2 | semidirect |
| 2. #11763850 | C2 | semidirect |
| 3. D8×#595 | C2 | semidirect |
| 4. #11763819 | C2 | semidirect |
| 5. #11763801 | C2 | semidirect |
| 6. #11763772 | C2 | semidirect |
| 11. D4×#595 | C22 | semidirect |
| 15. C2×D8×C17 | C4 | semidirect |
| 16. C2×#63228 | C4 | semidirect |
| 17. D8×D17 | C4 | semidirect |
| 18. D8×D17 | C4 | semidirect |
| 21. C2×D136 | C4 | semidirect |
| 23. #10587547 | C22 | semidirect |
| 24. #10587534 | C22 | semidirect |
| 25. #10587533 | C22 | semidirect |
| 26. #10587532 | C22 | semidirect |
| 27. C8×#595 | C22 | semidirect |
| 30. C2×D4×C17 | C2×C4 | semidirect |
| 34. D4×D17 | C2×C4 | semidirect |
| 36. C2×D68 | C2×C4 | semidirect |
| 48. D8×C17 | C2×C4 | semidirect |
| 49. D8×C17 | C2×C4 | semidirect |
| 50. C2×C8×C17 | C2×C4 | semidirect |
| 51. #63228 | C2×C4 | semidirect |
| 52. #63228 | C2×C4 | semidirect |
| 53. C2×#3622 | C2×C4 | semidirect |
| 54. D136 | C2×C4 | semidirect |
| 55. D136 | C2×C4 | semidirect |
| 56. C8×D17 | C2×C4 | semidirect |
| 57. C8×D17 | C2×C4 | semidirect |
| 123. C2×D8 | #595 | semidirect |
| 136. C17 | #2948 | semidirect |
| 144. C2×D4 | C2×#595 | semidirect |
| 151. D8 | C2×#595 | semidirect |
| 152. D8 | C2×#595 | semidirect |
| 161. C2×C8 | C2×#595 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11763876 | 2 |
| #11763850 | 2 |
| D8×#595 | 2 |
| #11763819 | 2 |
| #11763801 | 2 |
| #11763772 | 2 |
| C2×D8×D17 | 2 |
| #2948 | 17 |