Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
334 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 334 conjugacy classes of subgroups — too many to draw. Only its 87 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. #16839789 | C4 | semidirect |
| 13. #16839789 | C4 | semidirect |
| 18. C4×#11758194 | C4 | semidirect |
| 19. C2×#14519688 | C4 | semidirect |
| 193. C61 | #12865 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21454470 | 2 |
| #21445923 | 2 |
| #21443949 | 2 |
| #21443947 | 2 |
| #21443941 | 2 |
| #21443939 | 2 |
| C61×#1827 | 2 |
| #12865 | 61 |