Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
410 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 410 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 |
|---|---|---|
| 1. #11763343 | C2 | semidirect |
| 2. #11763215 | C2 | semidirect |
| 3. #11763196 | C2 | semidirect |
| 4. #11763173 | C2 | semidirect |
| 5. #11763171 | C2 | semidirect |
| 6. #11763043 | C2 | semidirect |
| 7. #11763036 | C2 | semidirect |
| 8. #11762919 | C2 | semidirect |
| 9. #11762909 | C2 | semidirect |
| 10. C2×#10587474 | C2 | semidirect |
| 11. C17×#532 | C2 | semidirect |
| 110. #3622 | #41 | semidirect |
| 132. #532 | D17 | semidirect |
| 180. C17 | #3180 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11763343 | 2 |
| #11763215 | 2 |
| #11763196 | 2 |
| #11763173 | 2 |
| #11763171 | 2 |
| #11763043 | 2 |
| #11763036 | 2 |
| #11762919 | 2 |
| #11762909 | 2 |
| C2×#10587474 | 2 |
| C17×#532 | 2 |
| #3180 | 17 |