Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
470 conjugacy classes of subgroups; only the 155 normal subgroups are shown.
This group has 470 conjugacy classes of subgroups — too many to draw. Only its 155 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×#16840194 | C2 | semidirect |
| 2. #21448126 | C2 | direct (N × H) |
| 3. C2×#16839602 | C2 | semidirect |
| 4. C2×#16839600 | C2 | semidirect |
| 5. C2×#16839599 | C2 | semidirect |
| 6. C2×#16839597 | C2 | semidirect |
| 7. C22×#14519683 | C2 | semidirect |
| 8. C2×C61×#508 | C2 | semidirect |
| 11. #16840194 | C22 | semidirect |
| 15. #16839602 | C22 | semidirect |
| 16. #16839600 | C22 | semidirect |
| 17. #16839599 | C22 | semidirect |
| 18. #16839597 | C22 | semidirect |
| 21. C2×#14519683 | C22 | semidirect |
| 24. C61×#508 | C22 | semidirect |
| 126. C2×#508 | D61 | semidirect |
| 135. C2×C61 | #2262 | semidirect |
| 143. #508 | C2×D61 | semidirect |
| 158. C61 | C2×#2262 | semidirect |
| 257. C2 | #21448126 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16840194 | 2 |
| #21448126 | 2 |
| C2×#16839602 | 2 |
| C2×#16839600 | 2 |
| C2×#16839599 | 2 |
| C2×#16839597 | 2 |
| C22×#14519683 | 2 |
| C2×C61×#508 | 2 |
| C2×#2262 | 61 |