Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
388 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 388 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 |
|---|---|---|
| 3. #11763161 | C2 | semidirect |
| 4. #11763146 | C2 | semidirect |
| 5. #11763051 | C2 | semidirect |
| 6. #11763020 | C2 | semidirect |
| 7. #11762966 | C2 | semidirect |
| 8. C4×#63231 | C2 | semidirect |
| 10. #103×D17 | C2 | semidirect |
| 11. C17×#477 | C2 | semidirect |
| 90. D68 | Q16 | semidirect |
| 123. #477 | D17 | semidirect |
| 163. C17 | #3299 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11763520 | 2 |
| Q8×D68 | 2 |
| #11763161 | 2 |
| #11763146 | 2 |
| #11763051 | 2 |
| #11763020 | 2 |
| #11762966 | 2 |
| C4×#63231 | 2 |
| #11762874 | 2 |
| #103×D17 | 2 |
| C17×#477 | 2 |
| #3299 | 17 |