Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
642 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 642 conjugacy classes of subgroups — too many to draw. Only its 89 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 |
|---|---|---|
| 1. #21456734 | C2 | semidirect |
| 2. #21456272 | C2 | semidirect |
| 3. #21446658 | C2 | semidirect |
| 4. #21444411 | C2 | semidirect |
| 5. #21444236 | C2 | semidirect |
| 6. #21443708 | C2 | semidirect |
| 7. C61×#3253 | C2 | semidirect |
| 197. #3253 | D61 | semidirect |
| 234. C61 | #10104 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21456734 | 2 |
| #21456272 | 2 |
| #21446658 | 2 |
| #21444411 | 2 |
| #21444236 | 2 |
| #21443708 | 2 |
| C61×#3253 | 2 |
| #10104 | 61 |