Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
294 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 294 conjugacy classes of subgroups — too many to draw. Only its 88 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 |
|---|---|---|
| 23. #16839515 | C4 | semidirect |
| 24. #16839512 | C4 | semidirect |
| 25. #16839512 | C4 | semidirect |
| 26. C61×#335 | C4 | semidirect |
| 161. #335 | #6923 | semidirect |
| 166. C61 | #9632 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21461743 | 2 |
| #21461613 | 2 |
| #21461389 | 2 |
| #21461387 | 2 |
| #21460716 | 2 |
| #21444566 | 2 |
| #9632 | 61 |