Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
302 conjugacy classes of subgroups; only the 168 normal subgroups are shown.
This group has 302 conjugacy classes of subgroups — too many to draw. Only its 168 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. #21460735 | C2 | direct (N × H) |
| 23. C2×#11758185 | C8 | semidirect |
| 30. C2×C16×C61 | C8 | semidirect |
| 47. C16×C61 | C2×C8 | semidirect |
| 48. #11758185 | C2×C8 | semidirect |
| 76. C2×C61 | #1313 | semidirect |
| 90. C61 | C2×#1313 | semidirect |
| 99. C2×C16 | #92420 | semidirect |
| 123. C16 | C2×#92420 | semidirect |
| 146. C2 | #21460735 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16840651 | 2 |
| C2×#16840603 | 2 |
| #21460735 | 2 |
| C2×#16839537 | 2 |
| C2×#1313 | 61 |