Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
434 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 434 conjugacy classes of subgroups — too many to draw. Only its 113 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. #11763357 | C2 | semidirect |
| 2. #11763356 | C2 | semidirect |
| 3. #11763197 | C2 | semidirect |
| 4. #11763167 | C2 | semidirect |
| 5. #11763015 | C2 | semidirect |
| 6. #11763014 | C2 | semidirect |
| 7. #11763001 | C2 | semidirect |
| 8. #11762955 | C2 | semidirect |
| 9. #11762951 | C2 | semidirect |
| 10. #11762865 | C2 | semidirect |
| 11. C17×#459 | C2 | semidirect |
| 154. #459 | D17 | semidirect |
| 196. C17 | #3214 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11763357 | 2 |
| #11763356 | 2 |
| #11763197 | 2 |
| #11763167 | 2 |
| #11763015 | 2 |
| #11763014 | 2 |
| #11763001 | 2 |
| #11762955 | 2 |
| #11762951 | 2 |
| #11762865 | 2 |
| C17×#459 | 2 |
| #3214 | 17 |