Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
434 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 434 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. #11763359 | C2 | semidirect |
| 2. #11763196 | C2 | semidirect |
| 3. #11763171 | C2 | semidirect |
| 4. #11763014 | C2 | semidirect |
| 5. #11763004 | C2 | semidirect |
| 6. #11762952 | C2 | semidirect |
| 7. #11762866 | C2 | semidirect |
| 8. C17×#532 | C2 | semidirect |
| 113. #532 | D17 | semidirect |
| 150. C17 | #3214 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11763359 | 2 |
| #11763196 | 2 |
| #11763171 | 2 |
| #11763014 | 2 |
| #11763004 | 2 |
| #11762952 | 2 |
| #11762866 | 2 |
| C17×#532 | 2 |
| #3214 | 17 |