Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
418 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 418 conjugacy classes of subgroups — too many to draw. Only its 69 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. #21447963 | C2 | semidirect |
| 3. #21445215 | C2 | semidirect |
| 4. #21443865 | C2 | semidirect |
| 5. #21443781 | C2 | semidirect |
| 6. #21443775 | C2 | semidirect |
| 7. C61×#2240 | C2 | semidirect |
| 17. C4⋊#11758185 | C22 | semidirect |
| 19. #16839515 | C22 | semidirect |
| 21. C61×#500 | C22 | semidirect |
| 24. C4×C16×C61 | C22 | semidirect |
| 145. #2240 | D61 | semidirect |
| 159. #500 | C2×D61 | semidirect |
| 171. C4×C16 | C2×D61 | semidirect |
| 174. C61 | #12372 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21457494 | 2 |
| #21447963 | 2 |
| #21445215 | 2 |
| #21443865 | 2 |
| #21443781 | 2 |
| #21443775 | 2 |
| C61×#2240 | 2 |
| #12372 | 61 |