Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
368 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 368 conjugacy classes of subgroups — too many to draw. Only its 111 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. #125×D17 | C2 | semidirect |
| 3. #11763219 | C2 | semidirect |
| 4. #11763218 | C2 | semidirect |
| 5. #11763173 | C2 | semidirect |
| 6. #11763126 | C2 | semidirect |
| 7. #11763121 | C2 | semidirect |
| 8. #11763111 | C2 | semidirect |
| 9. #11763107 | C2 | semidirect |
| 10. #11762864 | C2 | semidirect |
| 11. C17×#490 | C2 | semidirect |
| 129. #490 | D17 | semidirect |
| 171. C17 | #3234 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11763357 | 2 |
| #125×D17 | 2 |
| #11763219 | 2 |
| #11763218 | 2 |
| #11763173 | 2 |
| #11763126 | 2 |
| #11763121 | 2 |
| #11763111 | 2 |
| #11763107 | 2 |
| #11762864 | 2 |
| C17×#490 | 2 |
| #3234 | 17 |