Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
262 conjugacy classes of subgroups; only the 118 normal subgroups are shown.
This group has 262 conjugacy classes of subgroups — too many to draw. Only its 118 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. #21460853 | C2 | semidirect |
| 3. #21460852 | C2 | semidirect |
| 24. C16×D61 | C8 | semidirect |
| 48. C16×C61 | C2×C8 | semidirect |
| 50. #11758185 | C2×C8 | semidirect |
| 87. D61 | #1372 | semidirect |
| 98. C61 | C2×#1372 | semidirect |
| 134. C16 | D61⋊C8 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D61⋊#335 | 2 |
| #21460853 | 2 |
| #21460852 | 2 |
| C4×C16×D61 | 2 |
| C2×#1372 | 61 |