Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
516 conjugacy classes of subgroups; only the 168 normal subgroups are shown.
This group has 516 conjugacy classes of subgroups — too many to draw. Only its 168 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 |
|---|---|---|
| 2. #11763758 | C2 | semidirect |
| 3. #11763754 | C2 | semidirect |
| 4. C4⋊C4×#595 | C2 | semidirect |
| 6. C42×#595 | C2 | semidirect |
| 14. C17×#126 | C4 | semidirect |
| 15. #10587584 | C4 | semidirect |
| 18. #10587565 | C4 | semidirect |
| 19. #10587562 | C4 | semidirect |
| 38. C4⋊C4×C17 | C2×C4 | semidirect |
| 40. C42×C17 | C2×C4 | semidirect |
| 44. C4⋊Dic17 | C2×C4 | semidirect |
| 45. #63225 | C2×C4 | semidirect |
| 46. #63225 | C2×C4 | semidirect |
| 47. C4×Dic17 | C2×C4 | semidirect |
| 81. #595 | #126 | direct (N × H) |
| 102. #126 | #595 | direct (N × H) |
| 115. C17 | C4×#126 | semidirect |
| 128. C4⋊C4 | C2×#595 | semidirect |
| 138. C42 | C2×#595 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11763759 | 2 |
| #11763758 | 2 |
| #11763754 | 2 |
| C4⋊C4×#595 | 2 |
| C22⋊C4×#595 | 2 |
| C42×#595 | 2 |
| #126×D17 | 2 |
| C4×#126 | 17 |