Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
402 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 402 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. C2×#16839590 | C2 | semidirect |
| 5. #21446604 | C2 | semidirect |
| 6. #21443928 | C2 | semidirect |
| 7. C61×#1379 | C2 | semidirect |
| 19. #16839570 | C4 | semidirect |
| 43. #14519713 | C2×C4 | semidirect |
| 60. C2×C16×C61 | C2×C4 | semidirect |
| 160. #1379 | D61 | semidirect |
| 185. C61 | #12946 | semidirect |
| 210. C2×C16 | C4×D61 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21454696 | 2 |
| C2×#16839590 | 2 |
| C2×#16839570 | 2 |
| #21447532 | 2 |
| #21446604 | 2 |
| #21443928 | 2 |
| C61×#1379 | 2 |
| #12946 | 61 |