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 |
| 34. C8×C17 | C4⋊C4 | semidirect |
| 35. #3622 | C4⋊C4 | semidirect |
| 42. C4×C17 | #106 | semidirect |
| 44. Dic17 | #106 | semidirect |
| 60. C4×C8 | #595 | semidirect |
| 61. C17 | #1844 | semidirect |
| 85. C8 | C4⋊#595 | semidirect |
| 93. C4 | #10587533 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10587533 | 2 |
| #11763755 | 2 |
| C4×C8×D17 | 2 |
| #1844 | 17 |