Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
856 conjugacy classes of subgroups; only the 218 normal subgroups are shown.
This group has 856 conjugacy classes of subgroups — too many to draw. Only its 218 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×#63243 | C2 | semidirect |
| 2. C22×C4×#595 | C2 | semidirect |
| 3. C2×#10587550 | C2 | direct (N × H) |
| 6. C22×Q8×C17 | C4 | semidirect |
| 9. C2×#63256 | C4 | semidirect |
| 12. C22×D68 | C4 | semidirect |
| 17. C2×C4×#595 | C22 | semidirect |
| 19. C2×#63243 | C22 | semidirect |
| 20. #10587550 | C22 | direct (N × H) |
| 26. C2×Q8×C17 | C2×C4 | semidirect |
| 33. #63256 | C2×C4 | semidirect |
| 38. C2×D68 | C2×C4 | semidirect |
| 47. C4×#595 | C23 | semidirect |
| 49. #63243 | C23 | semidirect |
| 59. Q8×C17 | C22×C4 | semidirect |
| 68. D68 | C22×C4 | semidirect |
| 78. C22×C17 | #104 | semidirect |
| 96. C2×C17 | C2×#104 | semidirect |
| 105. C22×Q8 | #595 | semidirect |
| 117. C17 | C22×#104 | semidirect |
| 126. C2×Q8 | C2×#595 | semidirect |
| 154. Q8 | C22×#595 | semidirect |
| 180. C22 | #10587550 | direct (N × H) |
| 191. C2 | C2×#10587550 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#63243 | 2 |
| C22×C4×#595 | 2 |
| C2×#10587550 | 2 |
| C22×#63256 | 2 |
| C22×#104 | 17 |