Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
384 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 384 conjugacy classes of subgroups — too many to draw. Only its 129 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 |
|---|---|---|
| 5. #11763102 | C2 | semidirect |
| 6. #11763017 | C2 | semidirect |
| 8. Q16×Dic17 | C2 | semidirect |
| 9. #11762901 | C2 | semidirect |
| 98. C2×Dic17 | Q16 | semidirect |
| 170. C17 | #3104 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11763361 | 2 |
| C2×Q8×Dic17 | 2 |
| #11763145 | 2 |
| #11763142 | 2 |
| #11763102 | 2 |
| #11763017 | 2 |
| #11762965 | 2 |
| Q16×Dic17 | 2 |
| #11762901 | 2 |
| #11762859 | 2 |
| C17×#451 | 2 |
| #3104 | 17 |