Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
380 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 109 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. #21447613 | C2 | semidirect |
| 4. #21446607 | C2 | semidirect |
| 5. #21443913 | C2 | semidirect |
| 6. #21443907 | C2 | semidirect |
| 18. #16839578 | C4 | semidirect |
| 19. #16839575 | C4 | semidirect |
| 166. C61 | #12942 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21454736 | 2 |
| #21447613 | 2 |
| #21447568 | 2 |
| #21446607 | 2 |
| #21443913 | 2 |
| #21443907 | 2 |
| C2×C61×#359 | 2 |
| #12942 | 61 |