Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
348 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 348 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. #11763366 | C2 | semidirect |
| 2. #11763113 | C2 | semidirect |
| 3. #11763104 | C2 | semidirect |
| 4. #11763099 | C2 | semidirect |
| 5. #11763065 | C2 | semidirect |
| 7. #11763028 | C2 | semidirect |
| 8. #11763019 | C2 | semidirect |
| 9. #11763014 | C2 | semidirect |
| 10. #11762833 | C2 | semidirect |
| 176. C17 | #3252 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11763366 | 2 |
| #11763113 | 2 |
| #11763104 | 2 |
| #11763099 | 2 |
| #11763065 | 2 |
| #11763053 | 2 |
| #11763028 | 2 |
| #11763019 | 2 |
| #11763014 | 2 |
| #11762833 | 2 |
| C17×#529 | 2 |
| #3252 | 17 |