Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
386 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 386 conjugacy classes of subgroups — too many to draw. Only its 87 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. #21447577 | C2 | semidirect |
| 3. #21447527 | C2 | semidirect |
| 4. #21446718 | C2 | semidirect |
| 5. #21446715 | C2 | semidirect |
| 6. #21443920 | C2 | semidirect |
| 7. C61×#2138 | C2 | semidirect |
| 175. #2138 | D61 | semidirect |
| 206. C61 | #13447 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21458953 | 2 |
| #21447577 | 2 |
| #21447527 | 2 |
| #21446718 | 2 |
| #21446715 | 2 |
| #21443920 | 2 |
| C61×#2138 | 2 |
| #13447 | 61 |