Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
492 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 109 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. #21454410 | C2 | semidirect |
| 3. #21447556 | C2 | semidirect |
| 4. C2×#16839571 | C2 | semidirect |
| 5. #21447448 | C2 | semidirect |
| 6. #21443933 | C2 | semidirect |
| 7. C61×#1383 | C2 | semidirect |
| 13. #16840038 | C4 | semidirect |
| 14. #16840033 | C4 | semidirect |
| 40. C2×Dic244 | C2×C4 | semidirect |
| 42. C2×D488 | C2×C4 | semidirect |
| 73. #108×C61 | C2×C4 | semidirect |
| 194. #1383 | D61 | semidirect |
| 222. C61 | #13005 | semidirect |
| 260. #108 | C4×D61 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21455540 | 2 |
| #21454410 | 2 |
| #21447556 | 2 |
| C2×#16839571 | 2 |
| #21447448 | 2 |
| #21443933 | 2 |
| C61×#1383 | 2 |
| #13005 | 61 |