Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
352 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 352 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 |
|---|---|---|
| 2. #21447575 | C2 | semidirect |
| 3. #21443878 | C2 | semidirect |
| 4. #21443864 | C2 | semidirect |
| 5. C61×#1567 | C2 | semidirect |
| 125. #1567 | D61 | semidirect |
| 148. C61 | #11986 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21456398 | 2 |
| #21447575 | 2 |
| #21443878 | 2 |
| #21443864 | 2 |
| C61×#1567 | 2 |
| #11986 | 61 |