Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
434 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 434 conjugacy classes of subgroups — too many to draw. Only its 107 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. #21446743 | C2 | semidirect |
| 3. #21444536 | C2 | semidirect |
| 5. #21443688 | C2 | semidirect |
| 6. #21443674 | C2 | semidirect |
| 26. C61×#501 | C4 | semidirect |
| 27. C61×#489 | C4 | semidirect |
| 204. #501 | Dic61 | semidirect |
| 205. #489 | Dic61 | semidirect |
| 227. C61 | #9377 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21454958 | 2 |
| #21446743 | 2 |
| #21444536 | 2 |
| #21444344 | 2 |
| #21443688 | 2 |
| #21443674 | 2 |
| C61×#3239 | 2 |
| #9377 | 61 |