Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
444 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 444 conjugacy classes of subgroups — too many to draw. Only its 113 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. #11763354 | C2 | semidirect |
| 2. C2×#10587633 | C2 | semidirect |
| 3. #11763195 | C2 | semidirect |
| 4. #11763170 | C2 | semidirect |
| 5. #11763027 | C2 | semidirect |
| 6. #11763026 | C2 | semidirect |
| 7. #11762948 | C2 | semidirect |
| 8. #11762945 | C2 | semidirect |
| 9. #11762942 | C2 | semidirect |
| 10. #11762863 | C2 | semidirect |
| 11. C17×#448 | C2 | semidirect |
| 15. C2×SD16×C17 | C22 | semidirect |
| 21. C2×#63230 | C22 | semidirect |
| 22. #10587626 | C22 | semidirect |
| 24. D4×Dic17 | C22 | semidirect |
| 31. #10587579 | C22 | semidirect |
| 32. #10587574 | C22 | semidirect |
| 35. C17×#103 | C22 | semidirect |
| 37. #10587506 | C22 | semidirect |
| 40. #10587486 | C22 | semidirect |
| 41. #10587485 | C22 | semidirect |
| 153. #448 | D17 | semidirect |
| 168. C2×SD16 | C2×D17 | semidirect |
| 189. #103 | C2×D17 | semidirect |
| 195. C17 | #3213 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11763354 | 2 |
| C2×#10587633 | 2 |
| #11763195 | 2 |
| #11763170 | 2 |
| #11763027 | 2 |
| #11763026 | 2 |
| #11762948 | 2 |
| #11762945 | 2 |
| #11762942 | 2 |
| #11762863 | 2 |
| C17×#448 | 2 |
| #3213 | 17 |