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. #10587534 | 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 |
| 49. C8×C17 | C42 | semidirect |
| 51. #3622 | C42 | semidirect |
| 60. C4×C17 | #107 | semidirect |
| 64. Dic17 | #107 | semidirect |
| 84. C4×C8 | #595 | semidirect |
| 86. C17 | C4×#107 | semidirect |
| 122. C8 | C4×#595 | semidirect |
| 133. C4 | #10587534 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10587534 | 2 |
| C4×C4⋊#595 | 2 |
| #11763683 | 2 |
| C4×C8×D17 | 2 |
| C4×#107 | 17 |