Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
832 conjugacy classes of subgroups; only the 188 normal subgroups are shown.
This group has 832 conjugacy classes of subgroups — too many to draw. Only its 188 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. #11763761 | C2 | semidirect |
| 3. #11763757 | C2 | semidirect |
| 4. C4×C4⋊#595 | C2 | semidirect |
| 15. C17×#127 | C4 | semidirect |
| 16. #10587626 | C4 | semidirect |
| 17. #10587626 | C4 | semidirect |
| 18. #10587560 | C4 | semidirect |
| 26. C2×D4×C17 | C2×C4 | semidirect |
| 27. C2×D4×C17 | C2×C4 | semidirect |
| 28. C2×C22⋊D17 | C2×C4 | semidirect |
| 29. C2×C22⋊D17 | C2×C4 | semidirect |
| 34. C2×D68 | C2×C4 | semidirect |
| 35. C2×D68 | C2×C4 | semidirect |
| 41. C4⋊#595 | D4 | semidirect |
| 43. C42×C17 | C2×C4 | semidirect |
| 44. C4×Dic17 | C2×C4 | semidirect |
| 45. C4×Dic17 | C2×C4 | semidirect |
| 90. C4×C17 | C4×D4 | semidirect |
| 92. Dic17 | C4×D4 | semidirect |
| 111. #127 | #595 | semidirect |
| 120. C17 | #2366 | semidirect |
| 130. C2×D4 | C2×#595 | semidirect |
| 131. C2×D4 | C2×#595 | semidirect |
| 145. C42 | C2×#595 | semidirect |
| 191. C4 | D4×#595 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D4×#595 | 2 |
| #11763761 | 2 |
| #11763757 | 2 |
| C4×C4⋊#595 | 2 |
| #127×D17 | 2 |
| #2366 | 17 |