Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
380 conjugacy classes of subgroups; only the 80 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 80 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. #11763751 | C2 | semidirect |
| 3. #11763687 | C2 | semidirect |
| 5. C23×C4×C17 | C4 | semidirect |
| 10. C2×C22⋊Dic17 | C4 | semidirect |
| 14. C2×#63225 | C4 | semidirect |
| 15. C2×C4×Dic17 | C4 | semidirect |
| 48. C23×C17 | C4⋊C4 | semidirect |
| 74. C2×Dic17 | C4⋊C4 | semidirect |
| 98. C4×C17 | #99 | semidirect |
| 116. C23×C4 | #595 | semidirect |
| 127. C17 | #1799 | semidirect |
| 164. C23 | C4⋊#595 | semidirect |
| 210. C4 | #10587551 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10587551 | 2 |
| #11763751 | 2 |
| #11763687 | 2 |
| C2×C4×C22⋊D17 | 2 |
| #1799 | 17 |