Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
404 conjugacy classes of subgroups; only the 130 normal subgroups are shown.
This group has 404 conjugacy classes of subgroups — too many to draw. Only its 130 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 |
|---|---|---|
| 3. #11763679 | C2 | semidirect |
| 9. #10587677 | C4 | semidirect |
| 14. C2×#63243 | C4 | semidirect |
| 16. C17×#117 | C4 | semidirect |
| 17. #10587612 | C4 | semidirect |
| 19. C4⋊C4×D17 | C4 | semidirect |
| 42. C4×#595 | C2×C4 | semidirect |
| 45. #63243 | C2×C4 | semidirect |
| 127. #117 | #595 | semidirect |
| 134. C17 | #1733 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#63243 | 2 |
| C2×#10587677 | 2 |
| #11763679 | 2 |
| #117×D17 | 2 |
| #1733 | 17 |