Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
412 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 412 conjugacy classes of subgroups — too many to draw. Only its 111 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. #21447584 | C2 | semidirect |
| 4. #21445942 | C2 | semidirect |
| 5. #21443934 | C2 | semidirect |
| 6. #21443920 | C2 | semidirect |
| 10. #16839874 | C4 | semidirect |
| 161. C61 | #12826 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21454671 | 2 |
| #21447584 | 2 |
| C2×#16839575 | 2 |
| #21445942 | 2 |
| #21443934 | 2 |
| #21443920 | 2 |
| C61×#2140 | 2 |
| #12826 | 61 |