Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
932 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 932 conjugacy classes of subgroups — too many to draw. Only its 131 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×#16839559 | C2 | semidirect |
| 2. #21446223 | C2 | semidirect |
| 4. #16840240 | C22 | semidirect |
| 6. C2×#14519696 | C22 | semidirect |
| 10. C61×H(3,𝔽4) | C4 | semidirect |
| 110. H(3,𝔽4) | Dic61 | semidirect |
| 119. C61 | #12774 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16839559 | 2 |
| #21446223 | 2 |
| C2×C61×H(3,𝔽4) | 2 |
| #12774 | 61 |