Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
248 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 248 conjugacy classes of subgroups — too many to draw. Only its 69 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. C16×Dic122 | C2 | semidirect |
| 3. #21445180 | C2 | semidirect |
| 4. #21443864 | C2 | semidirect |
| 5. C61×#1371 | C2 | semidirect |
| 50. C16×C61 | SD16 | semidirect |
| 64. Dic122 | D16 | semidirect |
| 85. #1371 | D61 | semidirect |
| 102. C61 | #12439 | semidirect |
| 137. C16 | #11758190 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21448069 | 2 |
| C16×Dic122 | 2 |
| #21445180 | 2 |
| #21443864 | 2 |
| C61×#1371 | 2 |
| #12439 | 61 |