Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
214 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 214 conjugacy classes of subgroups — too many to draw. Only its 99 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×C32×D61 | C2 | semidirect |
| 3. #21444014 | C2 | semidirect |
| 4. C22⋊#14519683 | C2 | semidirect |
| 5. #21443956 | C2 | semidirect |
| 6. C32×Dic61 | C2 | semidirect |
| 7. C22×C32×C61 | C2 | semidirect |
| 39. C32×C61 | D4 | semidirect |
| 66. C22⋊D61 | C32 | direct (N × H) |
| 80. C22×C61 | C2×C32 | semidirect |
| 84. C2×D61 | C2×C32 | semidirect |
| 90. Dic61 | C2×C32 | semidirect |
| 92. C22×C32 | D61 | semidirect |
| 116. C61 | D4×C32 | semidirect |
| 135. C32 | C22⋊D61 | direct (N × H) |
| 178. C22 | C32×D61 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C32×D61 | 2 |
| C16×C22⋊D61 | 2 |
| #21444014 | 2 |
| C22⋊#14519683 | 2 |
| #21443956 | 2 |
| C32×Dic61 | 2 |
| C22×C32×C61 | 2 |
| D4×C32 | 61 |