Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
936 conjugacy classes of subgroups; only the 155 normal subgroups are shown.
This group has 936 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×#16840512 | C2 | semidirect |
| 2. #21457005 | C2 | semidirect |
| 3. #21445128 | C2 | semidirect |
| 4. #21445115 | C2 | semidirect |
| 5. #21444443 | C2 | semidirect |
| 6. #21444420 | C2 | semidirect |
| 16. #16840168 | C22 | semidirect |
| 17. #16840126 | C22 | semidirect |
| 22. #16839503 | C22 | semidirect |
| 218. C61 | #18994 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16840512 | 2 |
| #21457005 | 2 |
| #21445128 | 2 |
| #21445115 | 2 |
| #21444443 | 2 |
| #21444420 | 2 |
| C61×#3153 | 2 |
| #18994 | 61 |