Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
306 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 306 conjugacy classes of subgroups — too many to draw. Only its 87 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. #21448044 | C2 | semidirect |
| 3. #21445412 | C2 | semidirect |
| 4. C16×#92418 | C2 | semidirect |
| 5. C61×#2252 | C2 | semidirect |
| 44. C16×C61 | SD16 | semidirect |
| 59. #92418 | D16 | semidirect |
| 70. #2252 | D61 | semidirect |
| 89. C61 | #12503 | semidirect |
| 119. C16 | #11758201 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21448069 | 2 |
| #21448044 | 2 |
| #21445412 | 2 |
| C16×#92418 | 2 |
| C61×#2252 | 2 |
| #12503 | 61 |