Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
284 conjugacy classes of subgroups; only the 58 normal subgroups are shown.
This group has 284 conjugacy classes of subgroups — too many to draw. Only its 58 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. #11763715 | C2 | direct (N × H) |
| 4. C22×Q8×C17 | C4 | semidirect |
| 8. #10587633 | C4 | semidirect |
| 11. C2×C4×Dic17 | C4 | semidirect |
| 19. C2×Q8×C17 | C2×C4 | semidirect |
| 33. C4×Dic17 | C2×C4 | semidirect |
| 77. C2×C17 | #354 | semidirect |
| 81. C22×Q8 | #595 | semidirect |
| 91. C17 | C2×#354 | semidirect |
| 96. C2×Q8 | C2×#595 | semidirect |
| 153. C2 | #11763715 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10587539 | 2 |
| #11763715 | 2 |
| C2×#10587633 | 2 |
| C2×#354 | 17 |