Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
456 conjugacy classes of subgroups; only the 152 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 152 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. #11763760 | C2 | semidirect |
| 3. #11763758 | C2 | semidirect |
| 5. #11763755 | C2 | semidirect |
| 6. #11763754 | 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 |
| 101. #126 | #595 | semidirect |
| 114. C17 | #2383 | semidirect |
| 129. C4⋊C4 | C2×#595 | semidirect |
| 137. C42 | C2×#595 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11763760 | 2 |
| #11763759 | 2 |
| #11763758 | 2 |
| #11763756 | 2 |
| #11763755 | 2 |
| #11763754 | 2 |
| #126×D17 | 2 |
| #2383 | 17 |