Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
582 conjugacy classes of subgroups; only the 118 normal subgroups are shown.
This group has 582 conjugacy classes of subgroups — too many to draw. Only its 118 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 |
|---|---|---|
| 3. #21461558 | C2 | semidirect |
| 4. #21460660 | C2 | semidirect |
| 7. C23×#92420 | C4 | semidirect |
| 10. C2×#14519844 | C4 | semidirect |
| 13. C2×C22⋊#92420 | C4 | semidirect |
| 15. C2×C4×#92420 | C4 | semidirect |
| 21. #16839487 | C4 | semidirect |
| 22. #16839486 | C4 | semidirect |
| 23. C61×#323 | C4 | semidirect |
| 106. C23×C61 | #97 | semidirect |
| 130. C2×Dic61 | #97 | semidirect |
| 140. #92420 | #99 | semidirect |
| 196. #323 | #6923 | semidirect |
| 197. C61 | #8160 | semidirect |
| 285. C23 | #14519831 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16840789 | 2 |
| #21461566 | 2 |
| #21461558 | 2 |
| #21460660 | 2 |
| #21444134 | 2 |
| #8160 | 61 |