Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
662 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 662 conjugacy classes of subgroups — too many to draw. Only its 81 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. #21456283 | C2 | semidirect |
| 2. #21455910 | C2 | semidirect |
| 3. #21444443 | C2 | semidirect |
| 4. #21444365 | C2 | semidirect |
| 5. #21444262 | C2 | semidirect |
| 6. #21443683 | C2 | semidirect |
| 7. C61×#2631 | C2 | semidirect |
| 42. #14519777 | D4 | semidirect |
| 43. #14519774 | D4 | semidirect |
| 58. #14519688 | D4 | semidirect |
| 59. C4×#92418 | D4 | semidirect |
| 223. #2631 | D61 | semidirect |
| 260. C61 | #10018 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21456283 | 2 |
| #21455910 | 2 |
| #21444443 | 2 |
| #21444365 | 2 |
| #21444262 | 2 |
| #21443683 | 2 |
| C61×#2631 | 2 |
| #10018 | 61 |