Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
448 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 448 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. #11763532 | C2 | semidirect |
| 3. #11763156 | C2 | semidirect |
| 4. #11763135 | C2 | semidirect |
| 5. #11763089 | C2 | semidirect |
| 6. #11763058 | C2 | semidirect |
| 7. #11763009 | C2 | semidirect |
| 8. #11762958 | C2 | semidirect |
| 9. #11762888 | C2 | semidirect |
| 10. #11762812 | C2 | semidirect |
| 11. C4×SD16×C17 | C2 | semidirect |
| 15. C4×Q8×C17 | C22 | semidirect |
| 17. #10587632 | C22 | semidirect |
| 18. C2×#63230 | C22 | semidirect |
| 20. C2×#63218 | C22 | semidirect |
| 23. #10587578 | C22 | semidirect |
| 28. #10587555 | C22 | semidirect |
| 30. C17×#106 | C22 | semidirect |
| 31. C17×#103 | C22 | semidirect |
| 33. C4×C8×C17 | C22 | semidirect |
| 35. #10587492 | C22 | semidirect |
| 36. #10587492 | C22 | semidirect |
| 37. #10587491 | C22 | semidirect |
| 38. #10587480 | C22 | semidirect |
| 39. #10587478 | C22 | semidirect |
| 40. C4⋊#3622 | C22 | semidirect |
| 138. C4×SD16 | D17 | semidirect |
| 161. C4×Q8 | C2×D17 | semidirect |
| 166. #106 | C2×D17 | semidirect |
| 168. #103 | C2×D17 | semidirect |
| 175. C4×C8 | C2×D17 | semidirect |
| 176. C17 | #3324 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11763532 | 2 |
| D4×D68 | 2 |
| #11763156 | 2 |
| #11763135 | 2 |
| #11763089 | 2 |
| #11763058 | 2 |
| #11763009 | 2 |
| #11762958 | 2 |
| #11762888 | 2 |
| #11762812 | 2 |
| C4×SD16×C17 | 2 |
| #3324 | 17 |