Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
560 conjugacy classes of subgroups; only the 221 normal subgroups are shown.
This group has 560 conjugacy classes of subgroups — too many to draw. Only its 221 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. #11762716 | C2 | semidirect |
| 2. #11762702 | C2 | semidirect |
| 4. C22⋊C4×Dic17 | C2 | semidirect |
| 5. #11762655 | C2 | semidirect |
| 10. C17×#124 | C4 | semidirect |
| 25. C2×Q8×C17 | C2×C4 | semidirect |
| 36. C22⋊C4×C17 | C2×C4 | semidirect |
| 37. C42×C17 | C2×C4 | semidirect |
| 95. #124 | Dic17 | semidirect |
| 107. C17 | #2372 | semidirect |
| 111. C2×Q8 | C2×Dic17 | semidirect |
| 125. C22⋊C4 | C2×Dic17 | semidirect |
| 128. C42 | C2×Dic17 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11762716 | 2 |
| #11762702 | 2 |
| #11762689 | 2 |
| C22⋊C4×Dic17 | 2 |
| #11762655 | 2 |
| C2×C17×#124 | 2 |
| #2372 | 17 |