Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
372 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 372 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. #11763544 | C2 | semidirect |
| 2. #11763191 | C2 | semidirect |
| 3. #11763183 | C2 | semidirect |
| 4. #11763031 | C2 | semidirect |
| 5. #11763021 | C2 | semidirect |
| 6. #11763016 | C2 | semidirect |
| 8. Q8×#3622 | C2 | semidirect |
| 9. C4×#63230 | C2 | semidirect |
| 10. C4×#63229 | C2 | semidirect |
| 11. C17×#556 | C2 | semidirect |
| 122. #556 | 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 |
| #11763191 | 2 |
| #11763183 | 2 |
| #11763031 | 2 |
| #11763021 | 2 |
| #11763016 | 2 |
| #11763004 | 2 |
| Q8×#3622 | 2 |
| C4×#63230 | 2 |
| C4×#63229 | 2 |
| C17×#556 | 2 |
| #3394 | 17 |