Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
3994 conjugacy classes of subgroups; only the 331 normal subgroups are shown.
This group has 3994 conjugacy classes of subgroups — too many to draw. Only its 331 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. C2×#16839907 | C2 | semidirect |
| 2. C2×#16839896 | C2 | semidirect |
| 3. #21451543 | C2 | semidirect |
| 4. #21445759 | C2 | semidirect |
| 5. #21445750 | C2 | semidirect |
| 6. #21445731 | C2 | semidirect |
| 7. C22×H(5,𝔽2)×C61 | C2 | semidirect |
| 8. C22×#11758201 | C22 | semidirect |
| 9. C22×#11758199 | C22 | semidirect |
| 10. C2×#14519751 | C22 | semidirect |
| 13. C2×#14519701 | C22 | semidirect |
| 14. C2×#14519698 | C22 | semidirect |
| 15. C2×#14519698 | C22 | semidirect |
| 16. C2×C22⋊#92418 | C22 | semidirect |
| 17. C2×C22⋊#92418 | C22 | semidirect |
| 20. #16839622 | C22 | semidirect |
| 55. C2×#41×C61 | D4 | semidirect |
| 66. C22×D4×C61 | D4 | semidirect |
| 191. C22×H(5,𝔽2) | D61 | semidirect |
| 224. C61 | #32884 | semidirect |
| 234. C2×#41 | C22⋊D61 | semidirect |
| 247. C22×D4 | C22⋊D61 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16839907 | 2 |
| C2×#16839896 | 2 |
| #21451543 | 2 |
| #21445759 | 2 |
| #21445750 | 2 |
| #21445731 | 2 |
| C22×H(5,𝔽2)×C61 | 2 |
| #32884 | 61 |