Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
394 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 394 conjugacy classes of subgroups — too many to draw. Only its 103 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×#16839584 | C2 | semidirect |
| 5. #21446610 | C2 | semidirect |
| 6. #21443906 | C2 | semidirect |
| 7. C61×#1383 | C2 | semidirect |
| 21. #16839568 | C4 | semidirect |
| 44. C2×#11758185 | C2×C4 | semidirect |
| 59. #108×C61 | C2×C4 | semidirect |
| 152. #1383 | 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 |
|---|---|
| #21454702 | 2 |
| C2×#16839584 | 2 |
| #21447569 | 2 |
| #21447546 | 2 |
| #21446610 | 2 |
| #21443906 | 2 |
| C61×#1383 | 2 |
| #12949 | 61 |