Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
354 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 354 conjugacy classes of subgroups — too many to draw. Only its 115 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 |
|---|---|---|
| 2. #11763520 | C2 | semidirect |
| 3. #11763212 | C2 | semidirect |
| 4. #11763153 | C2 | semidirect |
| 5. #11763121 | C2 | semidirect |
| 6. #11763105 | C2 | semidirect |
| 7. #11763054 | C2 | semidirect |
| 8. C4×#63229 | C2 | semidirect |
| 9. #11762886 | C2 | semidirect |
| 10. #11762848 | C2 | semidirect |
| 11. C17×#476 | C2 | semidirect |
| 123. #476 | D17 | semidirect |
| 162. C17 | #3357 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11763524 | 2 |
| #11763520 | 2 |
| #11763212 | 2 |
| #11763153 | 2 |
| #11763121 | 2 |
| #11763105 | 2 |
| #11763054 | 2 |
| C4×#63229 | 2 |
| #11762886 | 2 |
| #11762848 | 2 |
| C17×#476 | 2 |
| #3357 | 17 |