Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
234 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 234 conjugacy classes of subgroups — too many to draw. Only its 103 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. #16839538 | C4 | semidirect |
| 13. C4×#11758185 | C4 | semidirect |
| 126. C61 | #12893 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21447416 | 2 |
| #21445943 | 2 |
| #21443922 | 2 |
| #21443920 | 2 |
| #21443916 | 2 |
| #21443914 | 2 |
| C61×#1833 | 2 |
| #12893 | 61 |