Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
516 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 516 conjugacy classes of subgroups — too many to draw. Only its 149 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×#10587562 | C2 | semidirect |
| 3. #11762704 | C2 | semidirect |
| 4. #11762703 | C2 | semidirect |
| 5. #11762699 | C2 | semidirect |
| 6. C42×Dic17 | C2 | semidirect |
| 7. C2×C17×#126 | C2 | semidirect |
| 32. C42×C17 | D4 | semidirect |
| 75. Dic17 | #126 | semidirect |
| 77. C2×#126 | D17 | semidirect |
| 102. C17 | #2860 | semidirect |
| 120. C42 | C22⋊D17 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10587562 | 2 |
| #11762709 | 2 |
| #11762704 | 2 |
| #11762703 | 2 |
| #11762699 | 2 |
| C42×Dic17 | 2 |
| C2×C17×#126 | 2 |
| #2860 | 17 |