Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
890 conjugacy classes of subgroups; only the 159 normal subgroups are shown.
This group has 890 conjugacy classes of subgroups — too many to draw. Only its 159 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. #21447555 | C2 | semidirect |
| 2. #21447526 | C2 | semidirect |
| 3. #21447433 | C2 | semidirect |
| 4. #21445865 | C2 | semidirect |
| 6. C2×#14519717 | C22 | semidirect |
| 7. C22×#11758185 | C22 | semidirect |
| 8. #16839800 | C22 | semidirect |
| 20. C61×#575 | C4 | semidirect |
| 178. #575 | Dic61 | semidirect |
| 191. C61 | #12745 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21447555 | 2 |
| #21447526 | 2 |
| #21447433 | 2 |
| #21445865 | 2 |
| C61×#3584 | 2 |
| #12745 | 61 |