Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
498 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 498 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 |
|---|---|---|
| 2. #21454958 | C2 | semidirect |
| 3. #21446746 | C2 | semidirect |
| 4. #21444532 | C2 | semidirect |
| 5. #21443688 | C2 | semidirect |
| 6. #21443675 | C2 | semidirect |
| 7. C61×#1509 | C2 | semidirect |
| 9. #16840152 | C4 | semidirect |
| 10. #16840128 | C4 | semidirect |
| 213. #1509 | D61 | semidirect |
| 248. C61 | #9378 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21456834 | 2 |
| #21454958 | 2 |
| #21446746 | 2 |
| #21444532 | 2 |
| #21443688 | 2 |
| #21443675 | 2 |
| C61×#1509 | 2 |
| #9378 | 61 |