Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
516 conjugacy classes of subgroups; only the 229 normal subgroups are shown.
This group has 516 conjugacy classes of subgroups — too many to draw. Only its 229 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. #11762695 | C2 | semidirect |
| 3. #11762677 | C2 | semidirect |
| 4. C4⋊C4×Dic17 | C2 | semidirect |
| 6. C42×Dic17 | C2 | semidirect |
| 9. C17×#126 | C4 | semidirect |
| 30. C4⋊C4×C17 | C2×C4 | semidirect |
| 32. C42×C17 | C2×C4 | semidirect |
| 69. Dic17 | #126 | direct (N × H) |
| 82. #126 | Dic17 | direct (N × H) |
| 95. C17 | C4×#126 | semidirect |
| 105. C4⋊C4 | C2×Dic17 | semidirect |
| 111. C42 | C2×Dic17 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11762702 | 2 |
| #11762695 | 2 |
| #11762677 | 2 |
| C4⋊C4×Dic17 | 2 |
| C22⋊C4×Dic17 | 2 |
| C42×Dic17 | 2 |
| C2×C17×#126 | 2 |
| C4×#126 | 17 |