Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
536 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 536 conjugacy classes of subgroups — too many to draw. Only its 85 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 |
|---|---|---|
| 1. #21453781 | C2 | semidirect |
| 4. #21443644 | C2 | semidirect |
| 5. #21443644 | C2 | semidirect |
| 6. #21443642 | C2 | semidirect |
| 100. C2×Dic122 | SD16 | semidirect |
| 108. C4⋊C4×C61 | SD16 | semidirect |
| 243. C61 | #7748 | semidirect |
| 339. C4⋊C4 | #11758200 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21453781 | 2 |
| #21446907 | 2 |
| #21443644 | 2 |
| #21443642 | 2 |
| C61×#2041 | 2 |
| #7748 | 61 |