Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
234 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 234 conjugacy classes of subgroups — too many to draw. Only its 55 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. #21448068 | C2 | semidirect |
| 2. #21447896 | C2 | semidirect |
| 3. #21447892 | C2 | semidirect |
| 4. #21447655 | C2 | semidirect |
| 5. #21443894 | C2 | semidirect |
| 6. #21443855 | C2 | semidirect |
| 7. C61×#1357 | C2 | semidirect |
| 112. #1357 | D61 | semidirect |
| 133. C61 | #12436 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21448068 | 2 |
| #21447896 | 2 |
| #21447892 | 2 |
| #21447655 | 2 |
| #21443894 | 2 |
| #21443855 | 2 |
| C61×#1357 | 2 |
| #12436 | 61 |