Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
880 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 880 conjugacy classes of subgroups — too many to draw. Only its 105 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. C2×#10587505 | C2 | semidirect |
| 3. C2×#10587477 | C2 | semidirect |
| 4. #11762664 | C2 | semidirect |
| 5. C2×C17×#99 | C2 | semidirect |
| 6. C24×D17 | C4 | semidirect |
| 9. C22×C22⋊D17 | C4 | semidirect |
| 15. C22×D68 | C4 | semidirect |
| 16. C22×C4×D17 | C4 | semidirect |
| 17. C2×C22⋊C4×C17 | C22 | semidirect |
| 18. C2×C22⋊Dic17 | C22 | semidirect |
| 69. C23×C17 | C22⋊C4 | semidirect |
| 98. C22×D17 | C22⋊C4 | semidirect |
| 105. C2×C4×C17 | C22⋊C4 | semidirect |
| 113. C2×Dic17 | C22⋊C4 | semidirect |
| 146. C2×D17 | #99 | semidirect |
| 154. C2×#99 | D17 | semidirect |
| 179. C2×C22⋊C4 | C2×D17 | semidirect |
| 183. C17 | #1781 | semidirect |
| 254. C23 | #63227 | semidirect |
| 276. C2×C4 | #63227 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D4×D17 | 2 |
| C2×#10587505 | 2 |
| C2×#10587477 | 2 |
| #11762664 | 2 |
| C2×C17×#99 | 2 |
| #1781 | 17 |