Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
280 conjugacy classes of subgroups; only the 114 normal subgroups are shown.
This group has 280 conjugacy classes of subgroups — too many to draw. Only its 114 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 |
|---|---|---|
| 9. C4×C8×C17 | C4 | semidirect |
| 10. C8×Dic17 | C4 | semidirect |
| 11. C4×#3622 | C4 | semidirect |
| 35. C8×C17 | C4⋊C4 | semidirect |
| 36. #3622 | C4⋊C4 | semidirect |
| 44. C4×C17 | #107 | semidirect |
| 46. Dic17 | #107 | semidirect |
| 63. C4×C8 | #595 | semidirect |
| 64. C17 | #1845 | semidirect |
| 89. C8 | C4⋊#595 | semidirect |
| 98. C4 | #10587534 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10587534 | 2 |
| #11763755 | 2 |
| C4×C8×D17 | 2 |
| #1845 | 17 |