Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
560 conjugacy classes of subgroups; only the 160 normal subgroups are shown.
This group has 560 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. (C2×#595)⋊Q8 | C2 | semidirect |
| 2. #11763759 | C2 | semidirect |
| 4. C22⋊C4×#595 | C2 | semidirect |
| 5. #11763745 | C2 | semidirect |
| 15. C17×#124 | C4 | semidirect |
| 16. #10587633 | C4 | semidirect |
| 17. #10587622 | C4 | semidirect |
| 18. #10587571 | C4 | semidirect |
| 20. #10587561 | C4 | semidirect |
| 31. C2×Q8×C17 | C2×C4 | semidirect |
| 42. C2×Dic34 | C2×C4 | semidirect |
| 43. C2×Dic34 | C2×C4 | semidirect |
| 49. C22⋊C4×C17 | C2×C4 | semidirect |
| 50. C42×C17 | C2×C4 | semidirect |
| 51. C22⋊Dic17 | C2×C4 | semidirect |
| 52. #63227 | C2×C4 | semidirect |
| 53. #63227 | C2×C4 | semidirect |
| 54. C4×Dic17 | C2×C4 | semidirect |
| 55. C4×Dic17 | C2×C4 | semidirect |
| 126. #124 | #595 | semidirect |
| 138. C17 | #2372 | semidirect |
| 144. C2×Q8 | C2×#595 | semidirect |
| 163. C22⋊C4 | C2×#595 | semidirect |
| 168. C42 | C2×#595 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| (C2×#595)⋊Q8 | 2 |
| #11763759 | 2 |
| #11763757 | 2 |
| C22⋊C4×#595 | 2 |
| #11763745 | 2 |
| #124×D17 | 2 |
| #2372 | 17 |