Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
168 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 168 conjugacy classes of subgroups — too many to draw. Only its 51 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 |
|---|---|---|
| 7. C4×#3633 | C4 | semidirect |
| 16. C4×#595 | C8 | semidirect |
| 20. C42×C17 | C8 | semidirect |
| 22. C4×Dic17 | C8 | semidirect |
| 66. C17 | #1274 | semidirect |
| 79. C42 | #3633 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11763922 | 2 |
| #11763745 | 2 |
| #1274 | 17 |