Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
550 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 550 conjugacy classes of subgroups — too many to draw. Only its 97 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. #21455823 | C2 | semidirect |
| 3. #21446617 | C2 | semidirect |
| 4. #21444222 | C2 | semidirect |
| 5. #21444218 | C2 | semidirect |
| 6. #21443650 | C2 | semidirect |
| 7. C61×#3135 | C2 | semidirect |
| 200. #3135 | D61 | semidirect |
| 238. C61 | #10033 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21455823 | 2 |
| #21455815 | 2 |
| #21446617 | 2 |
| #21444222 | 2 |
| #21444218 | 2 |
| #21443650 | 2 |
| C61×#3135 | 2 |
| #10033 | 61 |