Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
514 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 514 conjugacy classes of subgroups — too many to draw. Only its 125 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×#10587616 | C2 | semidirect |
| 2. #11763127 | C2 | semidirect |
| 3. #11763125 | C2 | semidirect |
| 4. #11763060 | C2 | semidirect |
| 5. #11762943 | C2 | semidirect |
| 6. #11762942 | C2 | semidirect |
| 7. #11762773 | C2 | semidirect |
| 8. C2×C17×#121 | C2 | semidirect |
| 10. C22×D4×C17 | C22 | semidirect |
| 13. C22×D68 | C22 | semidirect |
| 17. C17×#121 | C22 | semidirect |
| 18. C2×C4⋊C4×C17 | C22 | semidirect |
| 20. C2×#63228 | C22 | semidirect |
| 24. #10587616 | C22 | semidirect |
| 26. C2×C4⋊Dic17 | C22 | semidirect |
| 27. C2×#63223 | C22 | semidirect |
| 28. #10587503 | C22 | semidirect |
| 29. C22⋊#3622 | C22 | semidirect |
| 30. C22⋊#3622 | C22 | semidirect |
| 31. #10587480 | C22 | semidirect |
| 32. #10587479 | C22 | semidirect |
| 132. C2×#121 | D17 | semidirect |
| 150. C22×D4 | C2×D17 | semidirect |
| 161. #121 | C2×D17 | semidirect |
| 163. C2×C4⋊C4 | C2×D17 | semidirect |
| 171. C17 | #3192 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10587616 | 2 |
| #11763127 | 2 |
| #11763125 | 2 |
| #11763060 | 2 |
| #11762943 | 2 |
| #11762942 | 2 |
| #11762773 | 2 |
| C2×C17×#121 | 2 |
| #3192 | 17 |