Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
224 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 224 conjugacy classes of subgroups — too many to draw. Only its 90 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 |
|---|---|---|
| 13. #10587535 | C4 | semidirect |
| 14. #10587532 | C4 | semidirect |
| 15. C17×#107 | C4 | semidirect |
| 16. #10587489 | C4 | semidirect |
| 17. #10587479 | C4 | semidirect |
| 82. #107 | #595 | semidirect |
| 87. C17 | #1773 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10587535 | 2 |
| #11763774 | 2 |
| C2×#10587532 | 2 |
| #11763679 | 2 |
| #11762846 | 2 |
| #1773 | 17 |