Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
492 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 141 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×#63219 | C2 | semidirect |
| 2. C2×#10587587 | C2 | semidirect |
| 3. #11763385 | C2 | semidirect |
| 5. #11763056 | C2 | semidirect |
| 6. #11763039 | C2 | semidirect |
| 7. #11762817 | C2 | semidirect |
| 8. #11762813 | C2 | semidirect |
| 9. C17×#427 | C2 | semidirect |
| 21. C2×#63218 | C22 | semidirect |
| 22. C2×C8×D17 | C22 | semidirect |
| 23. #10587583 | C22 | semidirect |
| 31. C17×#107 | C22 | semidirect |
| 32. C17×#106 | C22 | semidirect |
| 33. #10587481 | C22 | semidirect |
| 53. C2×C8×C17 | D4 | semidirect |
| 122. #427 | D17 | semidirect |
| 151. #107 | C2×D17 | semidirect |
| 152. #106 | C2×D17 | semidirect |
| 155. C17 | #3057 | semidirect |
| 180. C2×C8 | D68 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#63219 | 2 |
| C2×#10587587 | 2 |
| #11763385 | 2 |
| #11763378 | 2 |
| #11763056 | 2 |
| #11763039 | 2 |
| #11762817 | 2 |
| #11762813 | 2 |
| C17×#427 | 2 |
| #3057 | 17 |