Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
398 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 398 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. #11763440 | C2 | semidirect |
| 3. #11763111 | C2 | semidirect |
| 4. #11763107 | C2 | semidirect |
| 5. #11763097 | C2 | semidirect |
| 6. #11763087 | C2 | semidirect |
| 7. #11762849 | C2 | semidirect |
| 8. #11762847 | C2 | semidirect |
| 9. #11762835 | C2 | semidirect |
| 26. #10587576 | C22 | semidirect |
| 28. #10587574 | C22 | semidirect |
| 33. #10587489 | C22 | semidirect |
| 34. #10587489 | C22 | semidirect |
| 35. #10587488 | C22 | semidirect |
| 36. #10587488 | C22 | semidirect |
| 37. #10587485 | C22 | semidirect |
| 38. #10587485 | C22 | semidirect |
| 39. #10587479 | C22 | semidirect |
| 40. #10587478 | C22 | semidirect |
| 44. C2×D4×C17 | Q8 | semidirect |
| 165. C17 | #3081 | semidirect |
| 170. C2×D4 | Dic34 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11763440 | 2 |
| #11763284 | 2 |
| #11763111 | 2 |
| #11763107 | 2 |
| #11763097 | 2 |
| #11763087 | 2 |
| #11762849 | 2 |
| #11762847 | 2 |
| #11762835 | 2 |
| #11762814 | 2 |
| C2×C17×#102 | 2 |
| #3081 | 17 |