Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
1880 conjugacy classes of subgroups; only the 645 normal subgroups are shown.
This group has 1880 conjugacy classes of subgroups — too many to draw. Only its 645 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. C23×Dic34 | C2 | semidirect |
| 3. C2×#10587561 | C2 | direct (N × H) |
| 4. C22×#63227 | C2 | semidirect |
| 5. C22×C42×C17 | C2 | semidirect |
| 13. C22×Dic34 | C22 | semidirect |
| 14. C2×C42×C17 | C22 | semidirect |
| 15. C2×#63227 | C22 | semidirect |
| 16. #10587561 | C22 | direct (N × H) |
| 30. C2×Dic34 | C23 | semidirect |
| 31. C42×C17 | C23 | semidirect |
| 32. #63227 | C23 | semidirect |
| 49. C22×C17 | #124 | semidirect |
| 63. C22×C42 | D17 | semidirect |
| 64. C2×C17 | C2×#124 | semidirect |
| 78. C2×C42 | C2×D17 | semidirect |
| 79. C17 | C22×#124 | semidirect |
| 95. C42 | C22×D17 | semidirect |
| 114. C22 | #10587561 | direct (N × H) |
| 122. C2 | C2×#10587561 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×Dic34 | 2 |
| C23×D68 | 2 |
| C2×#10587561 | 2 |
| C22×#63227 | 2 |
| C22×C42×C17 | 2 |
| C22×#124 | 17 |