Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
444 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 444 conjugacy classes of subgroups — too many to draw. Only its 93 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. #11762813 | C2 | semidirect |
| 3. C2×#10587504 | C2 | semidirect |
| 4. #11762568 | C2 | semidirect |
| 5. C17×#518 | C2 | semidirect |
| 13. #10587626 | C4 | semidirect |
| 32. C2×D68 | C2×C4 | semidirect |
| 33. C4⋊C4×C17 | D4 | semidirect |
| 38. C4×Dic17 | C2×C4 | semidirect |
| 83. #518 | D17 | semidirect |
| 105. C17 | #1887 | semidirect |
| 124. C4⋊C4 | C22⋊D17 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10587626 | 2 |
| #11762813 | 2 |
| C2×#10587504 | 2 |
| #11762568 | 2 |
| C17×#518 | 2 |
| #1887 | 17 |