Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
718 conjugacy classes of subgroups; only the 211 normal subgroups are shown.
This group has 718 conjugacy classes of subgroups — too many to draw. Only its 211 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. #21454670 | C2 | semidirect |
| 3. #21447694 | C2 | semidirect |
| 4. #21447665 | C2 | semidirect |
| 5. #21447534 | C2 | semidirect |
| 6. #21447415 | C2 | semidirect |
| 7. C61×#2158 | C2 | semidirect |
| 10. C2×D976 | C4 | semidirect |
| 15. #16839844 | C22 | semidirect |
| 18. #16839562 | C22 | semidirect |
| 19. #16839537 | C22 | semidirect |
| 20. C16×Dic61 | C22 | semidirect |
| 23. C61×#367 | C22 | semidirect |
| 24. C61×#366 | C22 | semidirect |
| 28. C2×D488 | C2×C4 | semidirect |
| 35. D976 | C2×C4 | semidirect |
| 36. D976 | C2×C4 | semidirect |
| 44. C2×C16×C61 | C2×C4 | semidirect |
| 109. #2158 | D61 | semidirect |
| 128. #367 | C2×D61 | semidirect |
| 129. #366 | C2×D61 | semidirect |
| 133. C61 | #33456 | semidirect |
| 150. C2×C16 | C4×D61 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D976 | 2 |
| #21454670 | 2 |
| #21447694 | 2 |
| #21447665 | 2 |
| #21447534 | 2 |
| #21447415 | 2 |
| C61×#2158 | 2 |
| #33456 | 61 |