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. #11763661 | C2 | direct (N × H) |
| 7. C22×D68 | C4 | semidirect |
| 10. C2×C4⋊C4×C17 | C4 | semidirect |
| 14. #10587581 | C4 | semidirect |
| 17. (C2×#595)⋊C4 | C22 | semidirect |
| 19. #10587543 | C22 | semidirect |
| 35. C2×D68 | C2×C4 | semidirect |
| 44. C4⋊C4×C17 | C2×C4 | semidirect |
| 108. C2×C17 | #327 | semidirect |
| 125. C2×C4⋊C4 | #595 | semidirect |
| 131. C17 | C2×#327 | semidirect |
| 156. C4⋊C4 | C2×#595 | semidirect |
| 219. C2 | #11763661 | 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 |
| #11763661 | 2 |
| C2×#10587581 | 2 |
| C2×#327 | 17 |