Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
532 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 532 conjugacy classes of subgroups — too many to draw. Only its 81 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. #21456810 | C2 | semidirect |
| 2. #21455910 | C2 | semidirect |
| 3. #21444454 | C2 | semidirect |
| 4. #21444289 | C2 | semidirect |
| 5. #21444160 | C2 | semidirect |
| 6. #21443681 | C2 | semidirect |
| 7. C61×#3100 | C2 | semidirect |
| 202. #3100 | D61 | semidirect |
| 239. C61 | #10038 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21456810 | 2 |
| #21455910 | 2 |
| #21444454 | 2 |
| #21444289 | 2 |
| #21444160 | 2 |
| #21443681 | 2 |
| C61×#3100 | 2 |
| #10038 | 61 |