Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
356 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 356 conjugacy classes of subgroups — too many to draw. Only its 78 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. #21461934 | C2 | semidirect |
| 4. #21461031 | C2 | semidirect |
| 5. #21460716 | C2 | semidirect |
| 6. #21460653 | C2 | semidirect |
| 23. #16839508 | C4 | semidirect |
| 24. #16839505 | C4 | semidirect |
| 25. #16839505 | C4 | semidirect |
| 26. C61×#332 | C4 | semidirect |
| 189. #332 | #6923 | semidirect |
| 196. C61 | #9592 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21461982 | 2 |
| #21461934 | 2 |
| #21461166 | 2 |
| #21461031 | 2 |
| #21460716 | 2 |
| #21460653 | 2 |
| #21444467 | 2 |
| #9592 | 61 |