Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
394 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 394 conjugacy classes of subgroups — too many to draw. Only its 105 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. C2×#16839586 | C2 | semidirect |
| 5. #21443919 | C2 | semidirect |
| 6. #21443905 | C2 | semidirect |
| 7. C61×#1953 | C2 | semidirect |
| 20. #16839568 | C4 | semidirect |
| 45. C2×#11758185 | C2×C4 | semidirect |
| 59. #108×C61 | C2×C4 | semidirect |
| 151. #1953 | D61 | semidirect |
| 177. C61 | #12949 | semidirect |
| 207. #108 | C4×D61 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21454704 | 2 |
| C2×#16839586 | 2 |
| #21447566 | 2 |
| #21447546 | 2 |
| #21443919 | 2 |
| #21443905 | 2 |
| C61×#1953 | 2 |
| #12949 | 61 |