Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
1504 conjugacy classes of subgroups; only the 770 normal subgroups are shown.
This group has 1504 conjugacy classes of subgroups — too many to draw. Only its 770 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 | direct (N × H) |
| 2. C22×#63243 | C2 | semidirect |
| 3. C22×#63242 | C2 | semidirect |
| 12. #10587680 | C22 | direct (N × H) |
| 13. C2×#63243 | C22 | semidirect |
| 14. C2×#63242 | C22 | semidirect |
| 26. #63243 | C23 | semidirect |
| 27. #63242 | C23 | semidirect |
| 41. C22×C17 | #131 | semidirect |
| 52. C2×C17 | C2×#131 | semidirect |
| 65. C17 | C22×#131 | semidirect |
| 93. C22 | #10587680 | direct (N × H) |
| 99. C2 | C2×#10587680 | 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 |
| C22×#63243 | 2 |
| C22×#63242 | 2 |
| C22×#63256 | 2 |
| C22×#131 | 17 |