Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
404 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 404 conjugacy classes of subgroups — too many to draw. Only its 123 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. #11763537 | C2 | semidirect |
| 3. #11763181 | C2 | semidirect |
| 4. #11763180 | C2 | semidirect |
| 5. #11763015 | C2 | semidirect |
| 6. #11763012 | C2 | semidirect |
| 7. #11763008 | C2 | semidirect |
| 8. #11762933 | C2 | semidirect |
| 9. #11762900 | C2 | semidirect |
| 10. C4×#63230 | C2 | semidirect |
| 11. C17×#460 | C2 | semidirect |
| 102. Dic34 | SD16 | semidirect |
| 105. #3622 | #41 | semidirect |
| 131. #460 | D17 | semidirect |
| 169. C17 | #3392 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11763537 | 2 |
| #11763479 | 2 |
| #11763181 | 2 |
| #11763180 | 2 |
| #11763015 | 2 |
| #11763012 | 2 |
| #11763008 | 2 |
| #11762933 | 2 |
| #11762900 | 2 |
| C4×#63230 | 2 |
| C17×#460 | 2 |
| #3392 | 17 |