Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
362 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 362 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. C2×#10587555 | C2 | semidirect |
| 2. #11763219 | C2 | semidirect |
| 3. #11763168 | C2 | semidirect |
| 4. #11763137 | C2 | semidirect |
| 6. #11763104 | C2 | semidirect |
| 7. #11763099 | C2 | semidirect |
| 8. #11762866 | C2 | semidirect |
| 147. C17 | #3238 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10587555 | 2 |
| #11763219 | 2 |
| #11763168 | 2 |
| #11763137 | 2 |
| #11763120 | 2 |
| #11763104 | 2 |
| #11763099 | 2 |
| #11762866 | 2 |
| C17×#529 | 2 |
| #3238 | 17 |