Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
392 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 392 conjugacy classes of subgroups — too many to draw. Only its 121 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. #11763343 | C2 | semidirect |
| 2. #11763109 | C2 | semidirect |
| 3. #11763091 | C2 | semidirect |
| 4. #11763086 | C2 | semidirect |
| 5. #11763060 | C2 | semidirect |
| 6. #11763053 | C2 | semidirect |
| 7. #11763024 | C2 | semidirect |
| 8. #11763006 | C2 | semidirect |
| 9. #11763001 | C2 | semidirect |
| 10. #11762833 | C2 | semidirect |
| 11. C17×#532 | C2 | semidirect |
| 136. #532 | D17 | semidirect |
| 184. C17 | #3251 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11763343 | 2 |
| #11763109 | 2 |
| #11763091 | 2 |
| #11763086 | 2 |
| #11763060 | 2 |
| #11763053 | 2 |
| #11763024 | 2 |
| #11763006 | 2 |
| #11763001 | 2 |
| #11762833 | 2 |
| C17×#532 | 2 |
| #3251 | 17 |