Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
372 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 372 conjugacy classes of subgroups — too many to draw. Only its 133 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. #11763437 | C2 | semidirect |
| 3. #11763178 | C2 | semidirect |
| 4. #11763169 | C2 | semidirect |
| 5. #11763164 | C2 | semidirect |
| 6. #11763160 | C2 | semidirect |
| 7. #11762819 | C2 | semidirect |
| 10. C2×#10587487 | C2 | semidirect |
| 11. C17×#405 | C2 | semidirect |
| 133. #405 | D17 | semidirect |
| 168. C17 | #3137 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11763437 | 2 |
| #11763385 | 2 |
| #11763178 | 2 |
| #11763169 | 2 |
| #11763164 | 2 |
| #11763160 | 2 |
| #11762819 | 2 |
| #11762811 | 2 |
| #11762806 | 2 |
| C2×#10587487 | 2 |
| C17×#405 | 2 |
| #3137 | 17 |