Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
554 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 554 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 |
|---|---|---|
| 3. #21444500 | C2 | semidirect |
| 5. #21444214 | C2 | semidirect |
| 6. #21443722 | C2 | semidirect |
| 7. C61×#2568 | C2 | semidirect |
| 85. C2×Q8×C61 | SD16 | semidirect |
| 200. #2568 | D61 | semidirect |
| 234. C61 | #10244 | semidirect |
| 294. C2×Q8 | #11758201 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21456744 | 2 |
| #21455291 | 2 |
| #21444500 | 2 |
| #21444313 | 2 |
| #21444214 | 2 |
| #21443722 | 2 |
| C61×#2568 | 2 |
| #10244 | 61 |