Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
440 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 440 conjugacy classes of subgroups — too many to draw. Only its 145 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. #11763106 | C2 | semidirect |
| 3. #11763096 | C2 | semidirect |
| 4. #11763086 | C2 | semidirect |
| 5. #11762852 | C2 | semidirect |
| 6. #11762833 | C2 | semidirect |
| 8. C17×#533 | C2 | semidirect |
| 11. C17×C4⋊Q8 | C22 | semidirect |
| 12. C17×C4⋊Q8 | C22 | semidirect |
| 13. C17×#125 | C22 | semidirect |
| 29. #10587479 | C22 | semidirect |
| 30. #10587478 | C22 | semidirect |
| 31. C4⋊#3622 | C22 | semidirect |
| 32. C4⋊#3622 | C22 | semidirect |
| 42. C2×D68 | Q8 | semidirect |
| 111. #533 | D17 | semidirect |
| 127. C4⋊Q8 | C2×D17 | semidirect |
| 128. C4⋊Q8 | C2×D17 | semidirect |
| 129. #125 | C2×D17 | semidirect |
| 148. C17 | #3077 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×D68 | 2 |
| #11763106 | 2 |
| #11763096 | 2 |
| #11763086 | 2 |
| #11762852 | 2 |
| #11762833 | 2 |
| #11762813 | 2 |
| C17×#533 | 2 |
| #3077 | 17 |