Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
404 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 404 conjugacy classes of subgroups — too many to draw. Only its 88 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. C2×#10587549 | C2 | semidirect |
| 4. #11763682 | C2 | semidirect |
| 13. C17×C22⋊Q8 | C4 | semidirect |
| 14. #10587632 | C4 | semidirect |
| 15. #10587610 | C4 | semidirect |
| 16. #10587583 | C4 | semidirect |
| 30. C2×Q8×C17 | C2×C4 | semidirect |
| 44. C2×Dic34 | C2×C4 | semidirect |
| 52. C4⋊C4×C17 | C2×C4 | semidirect |
| 58. C4⋊Dic17 | C2×C4 | semidirect |
| 102. C22×C17 | #103 | semidirect |
| 110. C2×D17 | #103 | semidirect |
| 149. C22⋊Q8 | #595 | semidirect |
| 159. C17 | #1872 | semidirect |
| 165. C2×Q8 | C2×#595 | semidirect |
| 192. C4⋊C4 | C2×#595 | semidirect |
| 249. C22 | #10587549 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C4⋊#595 | 2 |
| C2×#10587549 | 2 |
| #11763777 | 2 |
| #11763682 | 2 |
| C22⋊Q8×D17 | 2 |
| #1872 | 17 |