Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
386 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 386 conjugacy classes of subgroups — too many to draw. Only its 125 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. C2×C4×Dic34 | C2 | semidirect |
| 3. #11763145 | C2 | semidirect |
| 5. #11763117 | C2 | semidirect |
| 6. #11763032 | C2 | semidirect |
| 7. #11762967 | C2 | semidirect |
| 9. #11762917 | C2 | semidirect |
| 10. #11762911 | C2 | semidirect |
| 11. C17×#432 | C2 | semidirect |
| 137. #432 | D17 | semidirect |
| 174. C17 | #3117 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11763343 | 2 |
| C2×C4×Dic34 | 2 |
| #11763145 | 2 |
| #11763128 | 2 |
| #11763117 | 2 |
| #11763032 | 2 |
| #11762967 | 2 |
| #11762950 | 2 |
| #11762917 | 2 |
| #11762911 | 2 |
| C17×#432 | 2 |
| #3117 | 17 |