Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
286 conjugacy classes of subgroups; only the 54 normal subgroups are shown.
This group has 286 conjugacy classes of subgroups — too many to draw. Only its 54 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×#10587539 | C2 | semidirect |
| 2. #11763715 | C2 | semidirect |
| 3. #11763713 | C2 | semidirect |
| 5. C2×#41×C17 | C4 | semidirect |
| 8. #10587633 | C4 | semidirect |
| 10. #10587626 | C4 | semidirect |
| 14. #10587612 | C4 | semidirect |
| 20. C2×Q8×C17 | C2×C4 | semidirect |
| 22. C2×D4×C17 | C2×C4 | semidirect |
| 37. C4×Dic17 | C2×C4 | semidirect |
| 38. C4×Dic17 | C2×C4 | semidirect |
| 91. C2×#41 | #595 | semidirect |
| 103. C17 | #2127 | semidirect |
| 106. C2×Q8 | C2×#595 | semidirect |
| 114. C2×D4 | C2×#595 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10587539 | 2 |
| #11763715 | 2 |
| #11763713 | 2 |
| #11763373 | 2 |
| #2127 | 17 |