Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
726 conjugacy classes of subgroups; only the 140 normal subgroups are shown.
This group has 726 conjugacy classes of subgroups — too many to draw. Only its 140 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. #21461947 | C2 | semidirect |
| 2. #21461755 | C2 | semidirect |
| 3. C8×D61⋊C8 | C2 | semidirect |
| 12. #16840139 | C4 | semidirect |
| 13. #16840138 | C4 | semidirect |
| 16. C61×#493 | C4 | semidirect |
| 58. D61⋊C8 | D8 | semidirect |
| 93. C8×C61 | #102 | semidirect |
| 94. #92418 | #102 | semidirect |
| 129. #493 | #6923 | semidirect |
| 136. C61 | #9824 | semidirect |
| 214. C8 | #14519839 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21461947 | 2 |
| #21461755 | 2 |
| C8×D61⋊C8 | 2 |
| #493×D61 | 2 |
| #9824 | 61 |