Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
438 conjugacy classes of subgroups; only the 148 normal subgroups are shown.
This group has 438 conjugacy classes of subgroups — too many to draw. Only its 148 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 |
|---|---|---|
| 15. #16839484 | C4 | semidirect |
| 16. #16839483 | C4 | semidirect |
| 17. C61×#322 | C4 | semidirect |
| 77. C8×C61 | #107 | semidirect |
| 79. #92418 | #107 | semidirect |
| 114. #322 | #6923 | semidirect |
| 115. C61 | #8820 | semidirect |
| 177. C8 | #14519846 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21461755 | 2 |
| #21461754 | 2 |
| #21461740 | 2 |
| #322×D61 | 2 |
| #8820 | 61 |