Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
472 conjugacy classes of subgroups; only the 162 normal subgroups are shown.
This group has 472 conjugacy classes of subgroups — too many to draw. Only its 162 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×#10587680 | C2 | semidirect |
| 2. C2×#10587678 | C2 | semidirect |
| 3. #11763852 | C2 | direct (N × H) |
| 4. C2×#10587535 | C2 | semidirect |
| 5. C2×#10587550 | C2 | semidirect |
| 6. C2×#10587548 | C2 | semidirect |
| 7. C2×C8×#595 | C2 | semidirect |
| 14. #10587680 | C22 | semidirect |
| 16. #10587678 | C22 | semidirect |
| 23. C2×SD16×C17 | C4 | semidirect |
| 24. C2×#63231 | C4 | semidirect |
| 25. C2×#63228 | C4 | semidirect |
| 26. #10587602 | C4 | semidirect |
| 28. C2×#63219 | C4 | semidirect |
| 30. #10587550 | C22 | semidirect |
| 31. #10587548 | C22 | semidirect |
| 32. #10587535 | C22 | semidirect |
| 33. C8×#595 | C22 | semidirect |
| 68. SD16×C17 | C2×C4 | semidirect |
| 70. #63231 | C2×C4 | semidirect |
| 71. #63228 | C2×C4 | semidirect |
| 73. #63219 | C2×C4 | semidirect |
| 136. C2×C17 | #443 | semidirect |
| 147. C2×SD16 | #595 | semidirect |
| 166. C17 | C2×#443 | semidirect |
| 187. SD16 | C2×#595 | semidirect |
| 263. C2 | #11763852 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10587680 | 2 |
| C2×#10587678 | 2 |
| #11763852 | 2 |
| C2×#10587535 | 2 |
| C2×#10587550 | 2 |
| C2×#10587548 | 2 |
| C2×C8×#595 | 2 |
| C2×#10587602 | 2 |
| C2×#443 | 17 |