Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
492 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 149 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. #11763380 | C2 | semidirect |
| 4. #11763055 | C2 | semidirect |
| 5. #11763038 | C2 | semidirect |
| 6. #11762847 | C2 | semidirect |
| 7. #11762819 | C2 | semidirect |
| 8. #11762815 | C2 | semidirect |
| 9. C2×C17×#131 | C2 | semidirect |
| 15. C2×M16×C17 | C22 | semidirect |
| 17. C22×C8×C17 | C22 | semidirect |
| 27. #10587610 | C22 | semidirect |
| 32. #10587489 | C22 | semidirect |
| 33. #10587488 | C22 | semidirect |
| 34. #10587487 | C22 | semidirect |
| 56. C2×C8×C17 | D4 | semidirect |
| 117. C2×#131 | D17 | semidirect |
| 138. C2×M16 | C2×D17 | semidirect |
| 140. C22×C8 | C2×D17 | semidirect |
| 155. C17 | #3057 | semidirect |
| 179. C2×C8 | C22⋊D17 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#63219 | 2 |
| #11763380 | 2 |
| #11763373 | 2 |
| #11763055 | 2 |
| #11763038 | 2 |
| #11762847 | 2 |
| #11762819 | 2 |
| #11762815 | 2 |
| C2×C17×#131 | 2 |
| #3057 | 17 |