Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
490 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 490 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. C2×#10587628 | C2 | semidirect |
| 2. C22×#63230 | C2 | semidirect |
| 4. #11763031 | C2 | semidirect |
| 5. #11763009 | C2 | semidirect |
| 6. #11762836 | C2 | semidirect |
| 7. #11762813 | C2 | semidirect |
| 8. #11762803 | C2 | semidirect |
| 9. C17×#519 | C2 | semidirect |
| 14. C4×Q8×C17 | C22 | semidirect |
| 18. C2×#63231 | C22 | semidirect |
| 22. C2×#63230 | C22 | semidirect |
| 29. #10587481 | C22 | semidirect |
| 31. #10587480 | C22 | semidirect |
| 32. C4⋊#3622 | C22 | semidirect |
| 36. C2×Q8×C17 | D4 | semidirect |
| 115. #519 | D17 | semidirect |
| 141. C4×Q8 | C2×D17 | semidirect |
| 149. C17 | #3043 | semidirect |
| 156. C2×Q8 | D68 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10587628 | 2 |
| C22×#63230 | 2 |
| #11763378 | 2 |
| #11763031 | 2 |
| #11763009 | 2 |
| #11762836 | 2 |
| #11762813 | 2 |
| #11762803 | 2 |
| C17×#519 | 2 |
| #3043 | 17 |