Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
840 conjugacy classes of subgroups; only the 338 normal subgroups are shown.
This group has 840 conjugacy classes of subgroups — too many to draw. Only its 338 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. #11763745 | C2 | direct (N × H) |
| 8. C2×C4×#595 | C4 | semidirect |
| 10. C2×C42×C17 | C4 | semidirect |
| 11. C2×C4×Dic17 | C4 | semidirect |
| 12. C2×C4×Dic17 | C4 | semidirect |
| 13. C42×D17 | C4 | semidirect |
| 30. C4×#595 | C2×C4 | semidirect |
| 31. C42×C17 | C2×C4 | semidirect |
| 32. C4×Dic17 | C2×C4 | semidirect |
| 33. C4×Dic17 | C2×C4 | semidirect |
| 72. C2×C17 | #376 | semidirect |
| 75. D17 | #376 | semidirect |
| 86. C2×C42 | #595 | semidirect |
| 88. C17 | C2×#376 | semidirect |
| 106. C42 | C2×#595 | semidirect |
| 142. C2 | #11763745 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C4×#595 | 2 |
| #11763745 | 2 |
| C2×(C2×#595)⋊C4 | 2 |
| C2×C42×D17 | 2 |
| C2×#376 | 17 |