Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
480 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 480 conjugacy classes of subgroups — too many to draw. Only its 157 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×#10587574 | C2 | semidirect |
| 3. #11763088 | C2 | direct (N × H) |
| 4. C2×#10587478 | C2 | semidirect |
| 5. C2×#10587485 | C2 | semidirect |
| 8. C2×C17×#107 | C2 | semidirect |
| 23. #10587574 | C22 | semidirect |
| 24. C17×#107 | C22 | semidirect |
| 26. #10587485 | C22 | semidirect |
| 28. #10587478 | C22 | semidirect |
| 38. C2×D68 | Q8 | semidirect |
| 79. D68 | C2×Q8 | semidirect |
| 105. C2×#107 | D17 | semidirect |
| 109. C2×C17 | #474 | semidirect |
| 130. #107 | C2×D17 | semidirect |
| 134. C17 | C2×#474 | semidirect |
| 207. C2 | #11763088 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10587574 | 2 |
| C2×#10587579 | 2 |
| #11763088 | 2 |
| C2×#10587478 | 2 |
| C2×#10587485 | 2 |
| C2×#10587492 | 2 |
| C2×#10587480 | 2 |
| C2×C17×#107 | 2 |
| C2×#474 | 17 |