Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
454 conjugacy classes of subgroups; only the 168 normal subgroups are shown.
This group has 454 conjugacy classes of subgroups — too many to draw. Only its 168 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 |
|---|---|---|
| 12. C8×#92418 | C4 | semidirect |
| 13. C8×#92418 | C4 | semidirect |
| 14. C8×#92418 | C4 | semidirect |
| 15. C82×C61 | C4 | semidirect |
| 70. C8×C61 | #106 | semidirect |
| 71. C8×C61 | #107 | semidirect |
| 73. #92418 | #106 | semidirect |
| 74. #92418 | #107 | semidirect |
| 107. C82 | #6923 | semidirect |
| 108. C61 | #8814 | semidirect |
| 166. C8 | #14519845 | semidirect |
| 167. 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 |
| C82×D61 | 2 |
| #8814 | 61 |