Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
1130 conjugacy classes of subgroups; only the 403 normal subgroups are shown.
This group has 1130 conjugacy classes of subgroups — too many to draw. Only its 403 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 |
|---|---|---|
| 2. #21448182 | C2 | semidirect |
| 3. C4×#14519708 | C2 | semidirect |
| 4. #21445652 | C2 | semidirect |
| 6. #21445506 | C2 | semidirect |
| 10. C4×#11758200 | C4 | semidirect |
| 30. C4×Dic122 | C2×C4 | semidirect |
| 35. #14519708 | C2×C4 | semidirect |
| 36. #14519700 | C2×C4 | semidirect |
| 39. C4×#92418 | C2×C4 | semidirect |
| 71. #11758200 | C42 | semidirect |
| 146. C61 | #20506 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×#11758200 | 2 |
| #21448182 | 2 |
| C4×#14519708 | 2 |
| #21445652 | 2 |
| #21445644 | 2 |
| #21445506 | 2 |
| C61×#2275 | 2 |
| #20506 | 61 |