Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
372 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 372 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 |
|---|---|---|
| 1. #11763545 | C2 | semidirect |
| 2. #11763529 | C2 | semidirect |
| 3. #11763192 | C2 | semidirect |
| 4. #11763181 | C2 | semidirect |
| 5. #11763030 | C2 | semidirect |
| 6. #11763022 | C2 | semidirect |
| 7. #11763020 | C2 | semidirect |
| 8. #11762933 | C2 | semidirect |
| 9. #11762900 | C2 | semidirect |
| 10. C4×#63229 | C2 | semidirect |
| 166. C17 | #3394 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11763545 | 2 |
| #11763529 | 2 |
| #11763192 | 2 |
| #11763181 | 2 |
| #11763030 | 2 |
| #11763022 | 2 |
| #11763020 | 2 |
| #11762933 | 2 |
| #11762900 | 2 |
| C4×#63229 | 2 |
| C17×#459 | 2 |
| #3394 | 17 |