Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
458 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 458 conjugacy classes of subgroups — too many to draw. Only its 71 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. #21447484 | C2 | semidirect |
| 3. #21443981 | C2 | semidirect |
| 4. C61×#2126 | C2 | semidirect |
| 7. C2×#14519774 | C4 | semidirect |
| 11. #16840136 | C4 | semidirect |
| 13. C4×#11758194 | C4 | semidirect |
| 15. #16839555 | C22 | semidirect |
| 19. C61×#353 | C22 | semidirect |
| 154. #2126 | D61 | semidirect |
| 176. #353 | C2×D61 | semidirect |
| 177. C61 | #13585 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21456272 | 2 |
| #21447484 | 2 |
| #21443981 | 2 |
| C61×#2126 | 2 |
| #13585 | 61 |