Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
362 conjugacy classes of subgroups; only the 143 normal subgroups are shown.
This group has 362 conjugacy classes of subgroups — too many to draw. Only its 143 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. #21447603 | C2 | semidirect |
| 3. #21443921 | C2 | semidirect |
| 13. C2×M32×C61 | C4 | semidirect |
| 15. C22×C16×C61 | C4 | semidirect |
| 99. C2×M32 | Dic61 | semidirect |
| 101. C22×C16 | Dic61 | semidirect |
| 108. C61 | #12839 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21447603 | 2 |
| #21445865 | 2 |
| #21443921 | 2 |
| C2×C61×#504 | 2 |
| #12839 | 61 |