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×#10587678 | C2 | direct (N × H) |
| 2. C22×#63243 | C2 | semidirect |
| 3. C22×#63247 | C2 | semidirect |
| 4. C22×#63242 | C2 | semidirect |
| 5. C23×#3624 | C2 | semidirect |
| 14. C2×#63247 | C22 | semidirect |
| 18. C22×#3624 | C22 | semidirect |
| 19. #10587678 | C22 | direct (N × H) |
| 20. C2×#63243 | C22 | semidirect |
| 21. C2×#63242 | C22 | semidirect |
| 36. #63247 | C23 | semidirect |
| 40. C2×#3624 | C23 | semidirect |
| 41. #63243 | C23 | semidirect |
| 42. #63242 | C23 | semidirect |
| 64. C22×C17 | #131 | semidirect |
| 80. C2×C17 | C2×#131 | semidirect |
| 98. C17 | C22×#131 | semidirect |
| 142. C22 | #10587678 | direct (N × H) |
| 151. C2 | C2×#10587678 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10587678 | 2 |
| C22×#63243 | 2 |
| C22×#63247 | 2 |
| C22×#63242 | 2 |
| C23×#3624 | 2 |
| C22×#63254 | 2 |
| C22×#131 | 17 |