Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
270 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 270 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. #21443889 | C2 | semidirect |
| 4. #21443888 | C2 | semidirect |
| 5. C61×#1370 | C2 | semidirect |
| 77. C8×C61 | M32 | semidirect |
| 84. #92418 | M32 | semidirect |
| 102. #1370 | D61 | semidirect |
| 118. C61 | #12004 | semidirect |
| 184. C8 | #14519716 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21447573 | 2 |
| C82×D61 | 2 |
| #21443889 | 2 |
| #21443888 | 2 |
| C61×#1370 | 2 |
| #12004 | 61 |