Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
248 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 248 conjugacy classes of subgroups — too many to draw. Only its 71 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. Q8×#11758185 | C2 | semidirect |
| 3. #21445179 | C2 | semidirect |
| 4. #21443890 | C2 | semidirect |
| 5. #21443865 | C2 | semidirect |
| 6. #21443864 | C2 | semidirect |
| 7. C61×#1668 | C2 | semidirect |
| 71. #11758185 | SD16 | semidirect |
| 75. Q8×C61 | D16 | semidirect |
| 115. #1668 | D61 | semidirect |
| 139. C61 | #12439 | semidirect |
| 192. Q8 | #14519718 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21448068 | 2 |
| Q8×#11758185 | 2 |
| #21445179 | 2 |
| #21443890 | 2 |
| #21443865 | 2 |
| #21443864 | 2 |
| C61×#1668 | 2 |
| #12439 | 61 |