Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
454 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 454 conjugacy classes of subgroups — too many to draw. Only its 109 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 |
|---|---|---|
| 9. #16840141 | C4 | semidirect |
| 10. #16840114 | C4 | semidirect |
| 91. C42×C61 | Q16 | semidirect |
| 192. C61 | #9297 | semidirect |
| 268. C42 | #11758202 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21456764 | 2 |
| #21448567 | 2 |
| #21444501 | 2 |
| #21444383 | 2 |
| #21443679 | 2 |
| #21443648 | 2 |
| C61×#1995 | 2 |
| #9297 | 61 |