Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
1072 conjugacy classes of subgroups; only the 175 normal subgroups are shown.
This group has 1072 conjugacy classes of subgroups — too many to draw. Only its 175 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. #21456368 | C2 | semidirect |
| 3. #21455637 | C2 | semidirect |
| 4. #21447029 | C2 | semidirect |
| 5. #21446800 | C2 | semidirect |
| 6. #21446660 | C2 | semidirect |
| 7. #21446028 | C2 | semidirect |
| 8. #21445630 | C2 | semidirect |
| 9. C61×#2641 | C2 | semidirect |
| 137. #11758194 | #41 | semidirect |
| 198. #2641 | D61 | semidirect |
| 236. C61 | #25690 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21459693 | 2 |
| #21456368 | 2 |
| #21455637 | 2 |
| #21447029 | 2 |
| #21446800 | 2 |
| #21446660 | 2 |
| #21446028 | 2 |
| #21445630 | 2 |
| C61×#2641 | 2 |
| #25690 | 61 |