Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
302 conjugacy classes of subgroups; only the 144 normal subgroups are shown.
This group has 302 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 |
|---|---|---|
| 3. #21460736 | C2 | semidirect |
| 4. #21460735 | C2 | semidirect |
| 28. C16×D61 | C8 | semidirect |
| 49. C16×C61 | C2×C8 | semidirect |
| 50. #11758185 | C2×C8 | semidirect |
| 81. D61 | #1313 | semidirect |
| 94. C61 | C2×#1313 | semidirect |
| 127. C16 | D61⋊C8 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21462020 | 2 |
| #21461013 | 2 |
| #21460736 | 2 |
| #21460735 | 2 |
| #346×D61 | 2 |
| C2×#1313 | 61 |