Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
398 conjugacy classes of subgroups; only the 112 normal subgroups are shown.
This group has 398 conjugacy classes of subgroups — too many to draw. Only its 112 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×#16840684 | C2 | semidirect |
| 2. C2×#16840603 | C2 | semidirect |
| 3. #21460784 | C2 | direct (N × H) |
| 8. #16840684 | C22 | semidirect |
| 10. #16840603 | C22 | semidirect |
| 29. #14519799 | C8 | semidirect |
| 31. C2×Dic244 | C8 | semidirect |
| 33. C2×D488 | C8 | semidirect |
| 83. Dic244 | C2×C8 | semidirect |
| 85. D488 | C2×C8 | semidirect |
| 143. C2×C61 | #1336 | semidirect |
| 161. C61 | C2×#1336 | semidirect |
| 281. C2 | #21460784 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16840684 | 2 |
| C2×#16840603 | 2 |
| #21460784 | 2 |
| C2×#16839878 | 2 |
| C2×#1336 | 61 |