Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
524 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 524 conjugacy classes of subgroups — too many to draw. Only its 165 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. #11762740 | C2 | semidirect |
| 3. #11762739 | C2 | semidirect |
| 4. #11762729 | C2 | semidirect |
| 5. #11762728 | C2 | semidirect |
| 38. C22×Dic17 | Q8 | semidirect |
| 129. C17 | #2659 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10587610 | 2 |
| #11762740 | 2 |
| #11762739 | 2 |
| #11762729 | 2 |
| #11762728 | 2 |
| #11762667 | 2 |
| C2×#10587502 | 2 |
| C2×C17×C22⋊Q8 | 2 |
| #2659 | 17 |