Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
982 conjugacy classes of subgroups; only the 199 normal subgroups are shown.
This group has 982 conjugacy classes of subgroups — too many to draw. Only its 199 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 |
|---|---|---|
| 1. #494×D61 | C2 | semidirect |
| 3. #486×D61 | C2 | semidirect |
| 4. #21445426 | C2 | semidirect |
| 5. #21445425 | C2 | semidirect |
| 6. #21445424 | C2 | semidirect |
| 7. #21445423 | C2 | semidirect |
| 8. C82×D61 | C2 | semidirect |
| 9. C61×#1709 | C2 | semidirect |
| 14. #16840142 | C22 | semidirect |
| 15. #16840141 | C22 | semidirect |
| 20. #16840110 | C22 | semidirect |
| 21. #16840109 | C22 | semidirect |
| 22. #16840108 | C22 | semidirect |
| 27. C8×#92418 | C22 | semidirect |
| 28. C8×#92418 | C22 | semidirect |
| 29. C61×#494 | C22 | semidirect |
| 31. C61×#486 | C22 | semidirect |
| 32. C82×C61 | C22 | semidirect |
| 149. #1709 | D61 | direct (N × H) |
| 155. D61 | #1709 | direct (N × H) |
| 163. #494 | C2×D61 | semidirect |
| 172. #486 | C2×D61 | semidirect |
| 178. C82 | C2×D61 | semidirect |
| 179. C61 | C2×#1709 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #494×D61 | 2 |
| #493×D61 | 2 |
| #486×D61 | 2 |
| #21445426 | 2 |
| #21445425 | 2 |
| #21445424 | 2 |
| #21445423 | 2 |
| C82×D61 | 2 |
| C61×#1709 | 2 |
| C2×#1709 | 61 |