Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
262 conjugacy classes of subgroups; only the 144 normal subgroups are shown.
This group has 262 conjugacy classes of subgroups — too many to draw. Only its 144 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. #21460852 | C2 | direct (N × H) |
| 24. C2×C16×C61 | C8 | semidirect |
| 42. C16×C61 | C2×C8 | semidirect |
| 76. C2×C61 | #1372 | semidirect |
| 88. C61 | C2×#1372 | semidirect |
| 95. C2×C16 | #92420 | semidirect |
| 120. C16 | C2×#92420 | semidirect |
| 149. C2 | #21460852 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16840625 | 2 |
| #21460852 | 2 |
| C2×C16×Dic61 | 2 |
| C2×#1372 | 61 |