Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
1054 conjugacy classes of subgroups; only the 167 normal subgroups are shown.
This group has 1054 conjugacy classes of subgroups — too many to draw. Only its 167 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. #21446614 | C2 | semidirect |
| 2. #21445811 | C2 | semidirect |
| 3. #21444496 | C2 | semidirect |
| 4. #21444270 | C2 | semidirect |
| 6. #16839786 | C22 | semidirect |
| 7. C2×C4⋊#92418 | C22 | semidirect |
| 10. C2×C4×#92418 | C22 | semidirect |
| 215. C61 | #8353 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21446614 | 2 |
| #21445811 | 2 |
| #21444496 | 2 |
| #21444270 | 2 |
| C61×#3496 | 2 |
| #8353 | 61 |