Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
222 conjugacy classes of subgroups; only the 136 normal subgroups are shown.
This group has 222 conjugacy classes of subgroups — too many to draw. Only its 136 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. #21460931 | C2 | direct (N × H) |
| 4. #16840694 | C4 | semidirect |
| 6. C2×#14519827 | C4 | semidirect |
| 12. #14519827 | C2×C4 | semidirect |
| 70. C2×C61 | #1398 | semidirect |
| 80. C61 | C2×#1398 | semidirect |
| 135. C2 | #21460931 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16840694 | 2 |
| #21460931 | 2 |
| C2×#16839537 | 2 |
| C2×#1398 | 61 |