Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
428 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 428 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 |
|---|---|---|
| 1. #11763810 | C2 | semidirect |
| 2. C2×#10587547 | C2 | semidirect |
| 3. C4×C4⋊#595 | C2 | semidirect |
| 11. C17×#127 | C4 | semidirect |
| 14. #10587626 | C4 | semidirect |
| 15. #10587560 | C4 | semidirect |
| 42. C4⋊#595 | D4 | semidirect |
| 97. C4×C17 | #102 | semidirect |
| 100. Dic17 | #102 | semidirect |
| 122. #127 | #595 | semidirect |
| 130. C17 | #1982 | semidirect |
| 210. C4 | #10587547 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11763810 | 2 |
| C2×#10587547 | 2 |
| C4×C4⋊#595 | 2 |
| #127×D17 | 2 |
| #1982 | 17 |