Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
752 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 752 conjugacy classes of subgroups — too many to draw. Only its 165 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×#10587637 | C2 | semidirect |
| 2. C22×#63229 | C2 | semidirect |
| 3. #11763380 | C2 | semidirect |
| 4. #11762971 | C2 | semidirect |
| 5. #11762960 | C2 | semidirect |
| 6. #11762814 | C2 | semidirect |
| 7. #11762805 | C2 | semidirect |
| 8. #11762776 | C2 | semidirect |
| 20. C22×Dic34 | C22 | semidirect |
| 23. C2×#63231 | C22 | semidirect |
| 27. C2×#63229 | C22 | semidirect |
| 28. C2×#63229 | C22 | semidirect |
| 29. #10587612 | C22 | semidirect |
| 30. #10587610 | C22 | semidirect |
| 31. C2×#63223 | C22 | semidirect |
| 32. C22×#3622 | C22 | semidirect |
| 33. #10587506 | C22 | semidirect |
| 34. #10587503 | C22 | semidirect |
| 35. #10587503 | C22 | semidirect |
| 36. C22⋊#3622 | C22 | semidirect |
| 183. C17 | #3009 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10587637 | 2 |
| C22×#63229 | 2 |
| #11763380 | 2 |
| #11762971 | 2 |
| #11762960 | 2 |
| #11762814 | 2 |
| #11762805 | 2 |
| #11762776 | 2 |
| C2×C17×H(5,𝔽2) | 2 |
| #3009 | 17 |