Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
190 conjugacy classes of subgroups; only the 80 normal subgroups are shown.
This group has 190 conjugacy classes of subgroups — too many to draw. Only its 80 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 |
|---|---|---|
| 3. #21460985 | C2 | direct (N × H) |
| 12. #16839595 | C4 | semidirect |
| 14. C2×#14519683 | C4 | semidirect |
| 15. C2×C32×C61 | C4 | semidirect |
| 28. #14519683 | C2×C4 | semidirect |
| 30. C32×C61 | C2×C4 | semidirect |
| 76. C2×C61 | #1426 | semidirect |
| 86. C2×C32 | #6923 | semidirect |
| 91. C61 | C2×#1426 | semidirect |
| 106. C32 | C2×#6923 | semidirect |
| 149. C2 | #21460985 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16840691 | 2 |
| C2×#16840689 | 2 |
| #21460985 | 2 |
| C2×#16839595 | 2 |
| C2×#1426 | 61 |