Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
716 conjugacy classes of subgroups; only the 163 normal subgroups are shown.
This group has 716 conjugacy classes of subgroups — too many to draw. Only its 163 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. C22×#14519722 | C2 | semidirect |
| 3. #21456314 | C2 | semidirect |
| 4. #21454670 | C2 | semidirect |
| 5. #21447873 | C2 | semidirect |
| 6. #21447863 | C2 | semidirect |
| 7. #21447577 | C2 | semidirect |
| 8. #21447538 | C2 | semidirect |
| 9. C61×#2138 | C2 | semidirect |
| 22. #16840145 | C22 | semidirect |
| 23. #16840140 | C22 | semidirect |
| 28. #16839580 | C22 | semidirect |
| 29. #16839565 | C22 | semidirect |
| 33. C61×#358 | C22 | semidirect |
| 34. C61×#357 | C22 | semidirect |
| 180. #2138 | D61 | semidirect |
| 209. #358 | C2×D61 | semidirect |
| 210. #357 | C2×D61 | semidirect |
| 211. C61 | #33586 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16840197 | 2 |
| C22×#14519722 | 2 |
| #21456314 | 2 |
| #21454670 | 2 |
| #21447873 | 2 |
| #21447863 | 2 |
| #21447577 | 2 |
| #21447538 | 2 |
| C61×#2138 | 2 |
| #33586 | 61 |