Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
760 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 760 conjugacy classes of subgroups — too many to draw. Only its 181 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×#63231 | C2 | semidirect |
| 2. C22×#63229 | C2 | semidirect |
| 3. C2×#10587610 | C2 | semidirect |
| 4. #11762971 | C2 | direct (N × H) |
| 5. C2×#10587506 | C2 | semidirect |
| 6. C2×#10587503 | C2 | semidirect |
| 7. C2×C22⋊#3622 | C2 | semidirect |
| 21. C2×#63231 | C22 | semidirect |
| 23. C2×#63229 | C22 | semidirect |
| 26. #10587610 | C22 | semidirect |
| 30. #10587506 | C22 | semidirect |
| 31. #10587503 | C22 | semidirect |
| 32. C22⋊#3622 | C22 | semidirect |
| 140. C2×C17 | #452 | semidirect |
| 168. C17 | C2×#452 | semidirect |
| 267. C2 | #11762971 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#63231 | 2 |
| C22×#63229 | 2 |
| C2×#10587610 | 2 |
| #11762971 | 2 |
| C2×#10587506 | 2 |
| C2×#10587503 | 2 |
| C2×C22⋊#3622 | 2 |
| C22×#41×C17 | 2 |
| C2×#452 | 17 |