Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
492 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 141 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. C22×#63230 | C2 | semidirect |
| 2. C2×#10587634 | C2 | semidirect |
| 4. #11763057 | C2 | semidirect |
| 5. #11763040 | C2 | semidirect |
| 6. #11762845 | C2 | semidirect |
| 7. #11762818 | C2 | semidirect |
| 8. #11762813 | C2 | semidirect |
| 9. C17×#536 | C2 | semidirect |
| 16. C17×C22⋊Q8 | C22 | semidirect |
| 28. C2×#63223 | C22 | semidirect |
| 30. C22×#3622 | C22 | semidirect |
| 31. #10587506 | C22 | semidirect |
| 33. #10587479 | C22 | semidirect |
| 34. #10587478 | C22 | semidirect |
| 67. C2×#3622 | D4 | semidirect |
| 118. #536 | D17 | semidirect |
| 146. C22⋊Q8 | C2×D17 | semidirect |
| 155. C17 | #3057 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#63230 | 2 |
| C2×#10587634 | 2 |
| #11763373 | 2 |
| #11763057 | 2 |
| #11763040 | 2 |
| #11762845 | 2 |
| #11762818 | 2 |
| #11762813 | 2 |
| C17×#536 | 2 |
| #3057 | 17 |