Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
460 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 460 conjugacy classes of subgroups — too many to draw. Only its 121 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 |
|---|---|---|
| 3. #21445621 | C2 | semidirect |
| 4. #21443947 | C2 | semidirect |
| 6. C2×#14519784 | C4 | semidirect |
| 10. #16839786 | C4 | semidirect |
| 12. #16839729 | C4 | semidirect |
| 15. C2×C4×#92418 | C4 | semidirect |
| 16. #16839561 | C4 | semidirect |
| 17. #16839559 | C4 | semidirect |
| 174. C61 | #12633 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21454531 | 2 |
| #21447504 | 2 |
| #21445621 | 2 |
| #21443947 | 2 |
| C61×#2126 | 2 |
| #12633 | 61 |