Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
508 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 508 conjugacy classes of subgroups — too many to draw. Only its 95 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. #21454853 | C2 | semidirect |
| 3. #21445645 | C2 | semidirect |
| 4. #21444429 | C2 | semidirect |
| 5. #21444315 | C2 | semidirect |
| 6. #21443676 | C2 | semidirect |
| 7. C61×#1302 | C2 | semidirect |
| 11. #16840053 | C4 | semidirect |
| 12. #16840053 | C4 | semidirect |
| 13. #16839958 | C4 | semidirect |
| 14. #16839958 | C4 | semidirect |
| 218. #1302 | D61 | semidirect |
| 253. C61 | #9163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21455911 | 2 |
| #21454853 | 2 |
| #21445645 | 2 |
| #21444429 | 2 |
| #21444315 | 2 |
| #21443676 | 2 |
| C61×#1302 | 2 |
| #9163 | 61 |