Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
280 conjugacy classes of subgroups; only the 110 normal subgroups are shown.
This group has 280 conjugacy classes of subgroups — too many to draw. Only its 110 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 |
|---|---|---|
| 11. #10587533 | C4 | direct (N × H) |
| 12. C4×C8×C17 | C4 | semidirect |
| 13. C8×Dic17 | C4 | semidirect |
| 14. C8×Dic17 | C4 | semidirect |
| 15. C4×#3622 | C4 | semidirect |
| 48. C8×C17 | C42 | semidirect |
| 50. #3622 | C42 | semidirect |
| 58. C4×C17 | #106 | semidirect |
| 62. Dic17 | #106 | semidirect |
| 81. C4×C8 | #595 | semidirect |
| 83. C17 | C4×#106 | semidirect |
| 118. C8 | C4×#595 | semidirect |
| 128. C4 | #10587533 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10587533 | 2 |
| C4×C4⋊#595 | 2 |
| #11763683 | 2 |
| C4×C8×D17 | 2 |
| C4×#106 | 17 |