Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
500 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 500 conjugacy classes of subgroups — too many to draw. Only its 149 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. C2×#10587637 | C2 | semidirect |
| 3. C2×#10587561 | C2 | semidirect |
| 4. #11763031 | C2 | semidirect |
| 5. #11763024 | C2 | semidirect |
| 6. #11762833 | C2 | semidirect |
| 7. #11762817 | C2 | semidirect |
| 8. #11762813 | C2 | semidirect |
| 9. C4×#41×C17 | C2 | semidirect |
| 13. C4×Q8×C17 | C22 | semidirect |
| 15. C4×D4×C17 | C22 | semidirect |
| 22. C2×#63231 | C22 | semidirect |
| 24. C2×#63229 | C22 | semidirect |
| 32. #10587481 | C22 | semidirect |
| 34. C4⋊#3622 | C22 | semidirect |
| 124. C4×#41 | D17 | semidirect |
| 149. C4×Q8 | C2×D17 | semidirect |
| 151. C4×D4 | C2×D17 | semidirect |
| 160. C17 | #3040 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10587637 | 2 |
| C2×#10587635 | 2 |
| C2×#10587561 | 2 |
| #11763031 | 2 |
| #11763024 | 2 |
| #11762833 | 2 |
| #11762817 | 2 |
| #11762813 | 2 |
| C4×#41×C17 | 2 |
| #3040 | 17 |