Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
388 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 388 conjugacy classes of subgroups — too many to draw. Only its 82 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×#10587543 | C2 | semidirect |
| 2. C2×(C2×#595)⋊C4 | C2 | semidirect |
| 3. #11763660 | C2 | direct (N × H) |
| 6. C22×D4×C17 | C4 | semidirect |
| 13. #10587624 | C4 | semidirect |
| 15. C2×C4⋊Dic17 | C4 | semidirect |
| 17. (C2×#595)⋊C4 | C22 | semidirect |
| 19. #10587543 | C22 | semidirect |
| 28. C2×D4×C17 | C2×C4 | semidirect |
| 46. C4⋊Dic17 | C2×C4 | semidirect |
| 109. C2×C17 | #327 | semidirect |
| 117. C22×D4 | #595 | semidirect |
| 131. C17 | C2×#327 | semidirect |
| 140. C2×D4 | C2×#595 | semidirect |
| 219. C2 | #11763660 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10587543 | 2 |
| C2×(C2×#595)⋊C4 | 2 |
| #11763660 | 2 |
| C2×#10587624 | 2 |
| C2×#327 | 17 |