Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
388 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 388 conjugacy classes of subgroups — too many to draw. Only its 103 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. #21447613 | C2 | semidirect |
| 5. #21446573 | C2 | semidirect |
| 6. #21443902 | C2 | semidirect |
| 7. C61×#1389 | C2 | semidirect |
| 18. #16839571 | C4 | semidirect |
| 144. #1389 | D61 | semidirect |
| 167. C61 | #12944 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16839883 | 2 |
| #21447613 | 2 |
| #21447554 | 2 |
| #21447548 | 2 |
| #21446573 | 2 |
| #21443902 | 2 |
| C61×#1389 | 2 |
| #12944 | 61 |