Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
396 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 396 conjugacy classes of subgroups — too many to draw. Only its 109 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. #11763360 | C2 | semidirect |
| 2. #11763344 | C2 | semidirect |
| 3. #11763201 | C2 | semidirect |
| 4. #11763198 | C2 | semidirect |
| 5. #11763175 | C2 | semidirect |
| 6. #11763034 | C2 | semidirect |
| 7. #11763027 | C2 | semidirect |
| 8. #11762974 | C2 | semidirect |
| 9. #11762957 | C2 | semidirect |
| 10. #11762864 | C2 | semidirect |
| 11. C17×#491 | C2 | semidirect |
| 139. #491 | D17 | semidirect |
| 183. C17 | #3219 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11763360 | 2 |
| #11763344 | 2 |
| #11763201 | 2 |
| #11763198 | 2 |
| #11763175 | 2 |
| #11763034 | 2 |
| #11763027 | 2 |
| #11762974 | 2 |
| #11762957 | 2 |
| #11762864 | 2 |
| C17×#491 | 2 |
| #3219 | 17 |