Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
698 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 698 conjugacy classes of subgroups — too many to draw. Only its 145 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×#10587694 | C2 | semidirect |
| 2. #11763609 | C2 | semidirect |
| 3. #11763383 | C2 | semidirect |
| 4. #11762994 | C2 | semidirect |
| 5. #11762984 | C2 | semidirect |
| 6. #11762825 | C2 | semidirect |
| 7. C2×C17×#101 | C2 | semidirect |
| 18. #10587633 | C22 | semidirect |
| 20. #10587630 | C22 | semidirect |
| 24. #10587595 | C22 | semidirect |
| 26. #10587594 | C22 | semidirect |
| 28. C17×#101 | C22 | semidirect |
| 29. #10587496 | C22 | semidirect |
| 124. C2×#101 | D17 | semidirect |
| 152. #101 | C2×D17 | semidirect |
| 153. C17 | #3020 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10587694 | 2 |
| #11763609 | 2 |
| #11763383 | 2 |
| #11762994 | 2 |
| #11762984 | 2 |
| #11762825 | 2 |
| C2×C17×#101 | 2 |
| #3020 | 17 |