Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
738 conjugacy classes of subgroups; only the 143 normal subgroups are shown.
This group has 738 conjugacy classes of subgroups — too many to draw. Only its 143 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. C22×Q8×D17 | C2 | semidirect |
| 2. C2×#10587604 | C2 | semidirect |
| 4. #11762964 | C2 | semidirect |
| 5. #11762963 | C2 | semidirect |
| 6. #11762950 | C2 | semidirect |
| 7. #11762949 | C2 | semidirect |
| 8. #11762948 | C2 | semidirect |
| 9. #11762816 | C2 | semidirect |
| 10. #11762771 | C2 | semidirect |
| 11. C17×#451 | C2 | semidirect |
| 23. C2×Q16×C17 | C22 | semidirect |
| 26. C2×#63231 | C22 | semidirect |
| 27. C2×#63230 | C22 | semidirect |
| 30. C2×#63219 | C22 | semidirect |
| 38. C17×#103 | C22 | semidirect |
| 40. #10587506 | C22 | semidirect |
| 43. #10587487 | C22 | semidirect |
| 44. #10587481 | C22 | semidirect |
| 61. Q8×D17 | D4 | semidirect |
| 142. C22×C17 | #137 | semidirect |
| 153. C2×D17 | #137 | semidirect |
| 168. #451 | D17 | semidirect |
| 194. C2×Q16 | C2×D17 | semidirect |
| 210. #103 | C2×D17 | semidirect |
| 214. C17 | #3004 | semidirect |
| 321. C22 | #10587604 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×Q8×D17 | 2 |
| C2×#10587604 | 2 |
| #11763322 | 2 |
| #11762964 | 2 |
| #11762963 | 2 |
| #11762950 | 2 |
| #11762949 | 2 |
| #11762948 | 2 |
| #11762816 | 2 |
| #11762771 | 2 |
| C17×#451 | 2 |
| #3004 | 17 |