Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
410 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 410 conjugacy classes of subgroups — too many to draw. Only its 121 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. C2×#10587561 | C2 | semidirect |
| 2. #11763191 | C2 | semidirect |
| 3. #11763166 | C2 | semidirect |
| 4. #11763031 | C2 | semidirect |
| 5. #11763024 | C2 | semidirect |
| 6. #11762964 | C2 | semidirect |
| 7. #11762959 | C2 | semidirect |
| 8. #11762947 | C2 | semidirect |
| 10. #11762862 | C2 | semidirect |
| 11. C17×#529 | C2 | semidirect |
| 15. C17×#125 | C22 | semidirect |
| 16. C17×#124 | C22 | semidirect |
| 20. C4×Q8×C17 | C22 | semidirect |
| 22. C4×D4×C17 | C22 | semidirect |
| 25. C2×#63231 | C22 | semidirect |
| 27. C2×#63229 | C22 | semidirect |
| 37. #10587481 | C22 | semidirect |
| 38. #10587481 | C22 | semidirect |
| 41. C4⋊#3622 | C22 | semidirect |
| 42. C4×#3622 | C22 | semidirect |
| 138. #529 | D17 | semidirect |
| 162. #125 | C2×D17 | semidirect |
| 167. #124 | C2×D17 | semidirect |
| 171. C4×Q8 | C2×D17 | semidirect |
| 173. C4×D4 | C2×D17 | semidirect |
| 186. C17 | #3211 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10587561 | 2 |
| #11763191 | 2 |
| #11763166 | 2 |
| #11763031 | 2 |
| #11763024 | 2 |
| #11762964 | 2 |
| #11762959 | 2 |
| #11762947 | 2 |
| #11762942 | 2 |
| #11762862 | 2 |
| C17×#529 | 2 |
| #3211 | 17 |