Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
400 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 400 conjugacy classes of subgroups — too many to draw. Only its 117 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. #11763365 | C2 | semidirect |
| 3. #11763170 | C2 | semidirect |
| 4. #11763167 | C2 | semidirect |
| 5. #11763166 | C2 | semidirect |
| 6. #11763164 | C2 | semidirect |
| 7. #11763163 | C2 | semidirect |
| 8. #11762816 | C2 | semidirect |
| 10. C4×#63218 | C2 | semidirect |
| 11. C17×#488 | C2 | semidirect |
| 14. C17×#125 | C22 | semidirect |
| 21. #10587574 | C22 | semidirect |
| 27. #10587556 | C22 | semidirect |
| 28. C17×#103 | C22 | semidirect |
| 30. C4×C8×C17 | C22 | semidirect |
| 31. #10587506 | C22 | semidirect |
| 34. #10587487 | C22 | semidirect |
| 35. #10587486 | C22 | semidirect |
| 36. #10587481 | C22 | semidirect |
| 38. C4×#3622 | C22 | semidirect |
| 118. #488 | D17 | semidirect |
| 132. #125 | C2×D17 | semidirect |
| 146. #103 | C2×D17 | semidirect |
| 153. C4×C8 | C2×D17 | semidirect |
| 154. C17 | #3140 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11763365 | 2 |
| #124×D17 | 2 |
| #11763170 | 2 |
| #11763167 | 2 |
| #11763166 | 2 |
| #11763164 | 2 |
| #11763163 | 2 |
| #11762816 | 2 |
| #11762812 | 2 |
| C4×#63218 | 2 |
| C17×#488 | 2 |
| #3140 | 17 |