Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
358 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 358 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 |
|---|---|---|
| 3. #11763116 | C2 | semidirect |
| 4. #11763019 | C2 | semidirect |
| 6. #11762914 | C2 | semidirect |
| 7. C4×#63231 | C2 | semidirect |
| 130. C17 | #3127 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11763421 | 2 |
| #11763150 | 2 |
| #11763116 | 2 |
| #11763019 | 2 |
| #11762965 | 2 |
| #11762914 | 2 |
| C4×#63231 | 2 |
| #11762870 | 2 |
| C17×#519 | 2 |
| #3127 | 17 |