Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
466 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 466 conjugacy classes of subgroups — too many to draw. Only its 115 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×#16839575 | C2 | semidirect |
| 2. #21447555 | C2 | semidirect |
| 3. #21447547 | C2 | semidirect |
| 4. #21447535 | C2 | semidirect |
| 5. #21447424 | C2 | semidirect |
| 6. #21445943 | C2 | semidirect |
| 24. C61×#495 | C4 | semidirect |
| 25. C61×#493 | C4 | semidirect |
| 32. #14519717 | D4 | semidirect |
| 34. C2×#11758185 | D4 | semidirect |
| 189. #495 | Dic61 | semidirect |
| 190. #493 | Dic61 | semidirect |
| 201. C61 | #13215 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16839575 | 2 |
| #21447555 | 2 |
| #21447547 | 2 |
| #21447535 | 2 |
| #21447424 | 2 |
| #21445943 | 2 |
| C61×#3155 | 2 |
| #13215 | 61 |