Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
456 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 88 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. #21461202 | C2 | semidirect |
| 4. #21461168 | C2 | semidirect |
| 5. #21460711 | C2 | semidirect |
| 6. #21460653 | C2 | semidirect |
| 26. #16840058 | C4 | semidirect |
| 27. #16840052 | C4 | semidirect |
| 28. #16840044 | C4 | semidirect |
| 32. C61×#474 | C4 | semidirect |
| 223. #474 | #6923 | semidirect |
| 241. C61 | #9209 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21462631 | 2 |
| #21461691 | 2 |
| #21461202 | 2 |
| #21461168 | 2 |
| #21460711 | 2 |
| #21460653 | 2 |
| #21455600 | 2 |
| #9209 | 61 |