Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
352 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 352 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 |
|---|---|---|
| 2. #11763205 | C2 | semidirect |
| 3. #11763147 | C2 | semidirect |
| 4. #11763133 | C2 | semidirect |
| 5. #11763104 | C2 | semidirect |
| 6. #11763086 | C2 | semidirect |
| 7. #11763040 | C2 | semidirect |
| 8. C4×#63230 | C2 | semidirect |
| 9. D4×#3622 | C2 | semidirect |
| 10. #11762845 | C2 | semidirect |
| 11. C17×#556 | C2 | semidirect |
| 116. #556 | D17 | semidirect |
| 161. C17 | #3340 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11763524 | 2 |
| #11763205 | 2 |
| #11763147 | 2 |
| #11763133 | 2 |
| #11763104 | 2 |
| #11763086 | 2 |
| #11763040 | 2 |
| C4×#63230 | 2 |
| D4×#3622 | 2 |
| #11762845 | 2 |
| C17×#556 | 2 |
| #3340 | 17 |