Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
372 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 372 conjugacy classes of subgroups — too many to draw. Only its 117 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. #11763544 | C2 | semidirect |
| 2. #11763529 | C2 | semidirect |
| 3. #11763190 | C2 | semidirect |
| 4. #11763182 | C2 | semidirect |
| 5. #11763034 | C2 | semidirect |
| 6. #11763023 | C2 | semidirect |
| 7. #11763019 | C2 | semidirect |
| 9. C8×Dic34 | C2 | semidirect |
| 10. #11762896 | C2 | semidirect |
| 11. C4×SD16×C17 | C2 | semidirect |
| 131. C4×SD16 | D17 | semidirect |
| 166. C17 | #3394 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11763544 | 2 |
| #11763529 | 2 |
| #11763190 | 2 |
| #11763182 | 2 |
| #11763034 | 2 |
| #11763023 | 2 |
| #11763019 | 2 |
| #11763004 | 2 |
| C8×Dic34 | 2 |
| #11762896 | 2 |
| C4×SD16×C17 | 2 |
| #3394 | 17 |