Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
336 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 336 conjugacy classes of subgroups — too many to draw. Only its 117 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. #11763538 | C2 | semidirect |
| 4. #11763160 | C2 | semidirect |
| 5. #11763119 | C2 | semidirect |
| 8. #11763019 | C2 | semidirect |
| 9. C8×Dic34 | C2 | semidirect |
| 10. #11762901 | C2 | semidirect |
| 156. C17 | #3364 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11763538 | 2 |
| #11763529 | 2 |
| #11763162 | 2 |
| #11763160 | 2 |
| #11763119 | 2 |
| #11763089 | 2 |
| #11763029 | 2 |
| #11763019 | 2 |
| C8×Dic34 | 2 |
| #11762901 | 2 |
| C4×SD16×C17 | 2 |
| #3364 | 17 |