Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
436 conjugacy classes of subgroups; only the 161 normal subgroups are shown.
This group has 436 conjugacy classes of subgroups — too many to draw. Only its 161 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 |
|---|---|---|
| 3. C2×C8×Dic17 | C2 | semidirect |
| 4. #11762564 | C2 | semidirect |
| 5. C17×#336 | C2 | semidirect |
| 14. #10587491 | C4 | semidirect |
| 26. C2×C4×D17 | C8 | semidirect |
| 30. C2×C8×C17 | C2×C4 | semidirect |
| 36. C2×#3622 | C2×C4 | semidirect |
| 71. C2×D17 | C4×C8 | semidirect |
| 76. Dic17 | C22⋊C8 | semidirect |
| 81. #336 | D17 | semidirect |
| 98. C17 | C4×C22⋊C8 | semidirect |
| 116. C2×C8 | C4×D17 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C42×D17 | 2 |
| C2×#10587491 | 2 |
| C2×C8×Dic17 | 2 |
| #11762564 | 2 |
| C17×#336 | 2 |
| C4×C22⋊C8 | 17 |