Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
194 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 194 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 |
|---|---|---|
| 3. #21444021 | C2 | semidirect |
| 4. #21444019 | C2 | semidirect |
| 14. C61×M64 | C4 | semidirect |
| 28. C32×C61 | C2×C4 | semidirect |
| 79. M64 | Dic61 | semidirect |
| 86. C61 | #13634 | semidirect |
| 99. C32 | C2×Dic61 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21447603 | 2 |
| C2×#16839588 | 2 |
| #21444021 | 2 |
| #21444019 | 2 |
| C2×C61×M64 | 2 |
| #13634 | 61 |