Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
348 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 348 conjugacy classes of subgroups — too many to draw. Only its 77 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. #21446813 | C2 | semidirect |
| 2. #21444587 | C2 | semidirect |
| 4. #21444421 | C2 | semidirect |
| 6. #21443690 | C2 | semidirect |
| 196. C61 | #10497 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21446813 | 2 |
| #21444587 | 2 |
| #21444541 | 2 |
| #21444421 | 2 |
| #21444411 | 2 |
| #21443690 | 2 |
| C61×#3234 | 2 |
| #10497 | 61 |