Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
510 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 510 conjugacy classes of subgroups — too many to draw. Only its 79 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. #21456826 | C2 | semidirect |
| 3. #21455823 | C2 | semidirect |
| 4. #21444287 | C2 | semidirect |
| 5. #21444159 | C2 | semidirect |
| 6. #21443680 | C2 | semidirect |
| 7. C61×#1537 | C2 | semidirect |
| 196. #1537 | D61 | semidirect |
| 231. C61 | #10039 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21456826 | 2 |
| #21455911 | 2 |
| #21455823 | 2 |
| #21444287 | 2 |
| #21444159 | 2 |
| #21443680 | 2 |
| C61×#1537 | 2 |
| #10039 | 61 |