Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
388 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 388 conjugacy classes of subgroups — too many to draw. Only its 109 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. #11763413 | C2 | semidirect |
| 2. #11763379 | C2 | semidirect |
| 3. #11763181 | C2 | semidirect |
| 4. #11763178 | C2 | semidirect |
| 5. #11763163 | C2 | semidirect |
| 6. #11763022 | C2 | semidirect |
| 7. #11763012 | C2 | semidirect |
| 8. #11762951 | C2 | semidirect |
| 9. #11762946 | C2 | semidirect |
| 10. #11762871 | C2 | semidirect |
| 11. C17×#496 | C2 | semidirect |
| 118. #496 | D17 | semidirect |
| 159. C17 | #3221 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11763413 | 2 |
| #11763379 | 2 |
| #11763181 | 2 |
| #11763178 | 2 |
| #11763163 | 2 |
| #11763022 | 2 |
| #11763012 | 2 |
| #11762951 | 2 |
| #11762946 | 2 |
| #11762871 | 2 |
| C17×#496 | 2 |
| #3221 | 17 |