Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
386 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 386 conjugacy classes of subgroups — too many to draw. Only its 123 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 |
|---|---|---|
| 2. D4×Dic34 | C2 | semidirect |
| 3. #11763160 | C2 | semidirect |
| 4. #11763151 | C2 | semidirect |
| 5. #11763105 | C2 | semidirect |
| 6. #11763055 | C2 | semidirect |
| 7. #11763015 | C2 | semidirect |
| 8. #11762950 | C2 | semidirect |
| 9. C4×#63219 | C2 | semidirect |
| 10. #11762819 | C2 | semidirect |
| 11. C17×#436 | C2 | semidirect |
| 131. #436 | D17 | semidirect |
| 167. C17 | #3329 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11763524 | 2 |
| D4×Dic34 | 2 |
| #11763160 | 2 |
| #11763151 | 2 |
| #11763105 | 2 |
| #11763055 | 2 |
| #11763015 | 2 |
| #11762950 | 2 |
| C4×#63219 | 2 |
| #11762819 | 2 |
| C17×#436 | 2 |
| #3329 | 17 |