Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
402 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 402 conjugacy classes of subgroups — too many to draw. Only its 75 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. #21446666 | C2 | semidirect |
| 3. #21444539 | C2 | semidirect |
| 4. #21444416 | C2 | semidirect |
| 5. #21444410 | C2 | semidirect |
| 6. #21443690 | C2 | semidirect |
| 7. C61×#1569 | C2 | semidirect |
| 185. #1569 | D61 | semidirect |
| 219. C61 | #10496 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21456808 | 2 |
| #21446666 | 2 |
| #21444539 | 2 |
| #21444416 | 2 |
| #21444410 | 2 |
| #21443690 | 2 |
| C61×#1569 | 2 |
| #10496 | 61 |