Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
492 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 133 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×#63230 | C2 | semidirect |
| 2. C2×#10587593 | C2 | semidirect |
| 3. #11763383 | C2 | semidirect |
| 5. #11763058 | C2 | semidirect |
| 6. #11763041 | C2 | semidirect |
| 7. #11762845 | C2 | semidirect |
| 8. #11762815 | C2 | semidirect |
| 9. C17×#419 | C2 | semidirect |
| 16. #10587632 | C22 | semidirect |
| 25. C2×#63218 | C22 | semidirect |
| 26. C2×C8×D17 | C22 | semidirect |
| 31. C17×#103 | C22 | semidirect |
| 33. #10587479 | C22 | semidirect |
| 34. #10587478 | C22 | semidirect |
| 66. C2×#3622 | D4 | semidirect |
| 123. #419 | D17 | semidirect |
| 153. #103 | C2×D17 | semidirect |
| 155. C17 | #3057 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#63230 | 2 |
| C2×#10587593 | 2 |
| #11763383 | 2 |
| #11763378 | 2 |
| #11763058 | 2 |
| #11763041 | 2 |
| #11762845 | 2 |
| #11762815 | 2 |
| C17×#419 | 2 |
| #3057 | 17 |