Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
360 conjugacy classes of subgroups; only the 198 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 198 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. #11763868 | C2 | semidirect |
| 2. #11763865 | C2 | semidirect |
| 3. C2×#10587538 | C2 | semidirect |
| 13. #10587538 | C22 | semidirect |
| 14. C2×#63216 | C22 | semidirect |
| 15. #10587530 | C22 | semidirect |
| 16. #10587529 | C22 | semidirect |
| 80. C17 | #3407 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11763868 | 2 |
| #11763865 | 2 |
| C2×#10587538 | 2 |
| C2×#10587593 | 2 |
| #3407 | 17 |